Research activity information

• Ferromagnetic Ising Model on the Hierarchical Pentagon Lattice

  Takumi Oshima, Tomotoshi Nishino

  Sep. 2024, Journal of the Physical Society of Japan

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Holographic Analysis of Boundary Correlation Functions for the Hyperbolic-Lattice Ising Model

  Kouichi Okunishi, Tomotoshi Nishino

  Sep. 2024, Progress of Theoretical and Experimental Physics

  Scientific journal


• Local and global magnetization on the Sierpiński carpet

  Jozef Genzor, Andrej Gendiar, Tomotoshi Nishino

  American Physical Society (APS), Apr. 2023, Physical Review E, 107(4) (4)

  [Refereed]

  Scientific journal


• Density matrix renormalization group, 30 years on

  Frank Verstraete, Tomotoshi Nishino, Ulrich Schollwöck, Mari Carmen Bañuls, Garnet K. Chan, Miles E. Stoudenmire

  Springer Science and Business Media LLC, Apr. 2023, Nature Reviews Physics, 5(5) (5), 273 - 276

  [Invited]

  Scientific journal


• Entanglement bipartitioning and tree tensor networks

  Kouichi Okunishi, Hiroshi Ueda, Tomotoshi Nishino

  Abstract We propose the entanglement bipartitioning approach to design an optimal network structure of the tree tensor network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of spin-cluster nodes so as to minimize the mutual information or the maximum loss of the entanglement entropy associated with the branch to be bipartitioned. We demonstrate that entanglement bipartitioning of up to 16 sites gives rise to nontrivial tree network structures for S = 1/2 Heisenberg models in one and two dimensions. The resulting TTNs enable us to obtain better variational energies, compared with standard TTNs such as the uniform matrix product state and perfect binary tree tensor network.

  Oxford University Press (OUP), Jan. 2023, Progress of Theoretical and Experimental Physics, 2023(2) (2)

  [Refereed]

  Scientific journal


• Automatic structural optimization of tree tensor networks

  Toshiya Hikihara, Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Tomotoshi Nishino

  American Physical Society (APS), Jan. 2023, Physical Review Research, 5(1) (1)

  [Refereed]

  Scientific journal


• Developments in the Tensor Network — from Statistical Mechanics to Quantum Entanglement

  Kouichi Okunishi, Tomotoshi Nishino, Hiroshi Ueda

  Physical Society of Japan, Jun. 2022, Journal of the Physical Society of Japan, 91(6) (6)

  [Refereed]

  Scientific journal


• Energy Scale Deformation on Regular Polyhedra

  Takuya Eguchi, Satoshi Oga, Hosho Katsura, Andrej Gendiar, Tomotoshi Nishino

  Physical Society of Japan, Mar. 2022, Journal of the Physical Society of Japan, 91(3) (3)

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Entanglement Entropy on the Boundary of the Square-Lattice ±J Ising Model

  Yoshinori Sasagawa, Hiroshi Ueda, Jozef Genzor, Andrej Gendiar, Tomotoshi Nishino

  Physical Society of Japan, Nov. 2020, Journal of the Physical Society of Japan, 89(11) (11), 114005 - 114005, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model

  Hiroshi Ueda, Kouichi Okunishi, Seiji Yunoki, Tomotoshi Nishino

  American Physical Society (APS), Sep. 2020, Physical Review E, 102(3) (3), 032130, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Finite- m scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model

  Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Roman Krčmár, Andrej Gendiar, Seiji Yunoki, Tomotoshi Nishino

  American Physical Society ({APS}), Jun. 2020, Physical Review E, 101(6) (6), 062111, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Entanglement-entropy study of phase transitions in six-state clock model

  Roman Krcmar, Andrej Gendiar, Tomotoshi Nishino

  2020, Acta Physica Polonica A, 137, 598, English

  [Refereed]

  International conference proceedings


• Tensor-network study of a quantum phase transition on the Sierpiński fractal

  Roman Krcmar, Jozef Genzor, Yoju Lee, Hana Čenčariková, Tomotoshi Nishino, Andrej Gendiar

  American Physical Society (APS), Dec. 2018, Physical Review E, 98(6) (6), 062114, English

  [Refereed]

  Scientific journal


• Critical behavior of the two-dimensional icosahedron model

  Hiroshi Ueda, Kouichi Okunishi, Roman Krčmár, Andrej Gendiar, Seiji Yunoki, Tomotoshi Nishino

  Dec. 2017, Physical Review E, 96(6) (6), 062112, English

  [Refereed]

  Scientific journal


• <講義ノート>テンソルネットワーク形式への入り口 --イジング模型のテンソルネットワーク表現から-- (第61回物性若手夏の学校 集中ゼミ)

  西野 友年

  第61回物性若手夏の学校 集中ゼミテンソルネットワーク形式(Tensor-Network Formulation) とは、量子力学の作用積分、場の理論の伝播関数・相関関数、あるいは統計力学の要である分配関数を、局所的な重率を表す「テンソルの縮約」で表現しようとする理論形式である。興味深いことに、初等的な統計力学で習う2次元イジング模型(2D Ising Model) のボルツマン重率は、自然な形でテンソルネットワークの一種である、バーテックス模型(Vertex Model) として記述できる。この事実を足がかりとして、まずはテンソルネットワーク形式に慣れ、「活用方法への発想」について足がかりを得ることが、本稿の目的である。以下では主として統計力学系に着目して話を進めるが、殆ど全ての内容について「量子・古典対応」(～経路積分) を通じ、そのまま量子物理学系へと持ち込むことができる。テンソルネットワークの重要な一例である行列積状態(Matrix-Product State, MPS) についてまず学び、局所的なテンソルの縮約が持つ汎用性を垣間見よう。テンソルネットワーク繰り込み群(Tensor Network Renormalization, TNR)など、最先端の研究へと至る経緯についても、概略を紹介する。

  物性研究・電子版 編集委員会, Nov. 2017, 物性研究・電子版, 6(4) (4), [1], Japanese


• Tensor Network Formulation : Developments and Applications

  西野 友年, 大久保 毅

  日本物理学会, Oct. 2017, 日本物理学会誌, 72(10) (10), 702 - 711, Japanese, Domestic magazine

  [Refereed]

  Scientific journal


• Tensor Networks: Phase transition phenomena on hyperbolic and fractal geometries

  Jozef Genzor, Tomotoshi Nishino, Andrej Gendiar

  2017, Acta Physics Slovaca, 67, 85 - 206, English

  [Refereed]

  Scientific journal


• Phase diagram of a truncated tetrahedral model

  Roman Krcmar, Andrej Gendiar, Tomotoshi Nishino

  Aug. 2016, Physical Review E, 94(2) (2), 022134, English

  [Refereed]

  Scientific journal


• Phase transition of the Ising model on a fractal lattice

  Jozef Genzor, Andrej Gendiar, Tomotoshi Nishino

  American Physical Society (APS), Jan. 2016, Physical Review E, 93(1) (1), 012141, English

  [Refereed]

  Scientific journal


• Time evolution within a comoving window: scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains

  V Zauner, M Ganahl, H G Evertz, T Nishino

  IOP Publishing, Oct. 2015, Journal of Physics: Condensed Matter, 27(42) (42), 425602, English

  [Refereed]

  Scientific journal


• Mean-field universality class induced by weak hyperbolic curvatures

  Andrej Gendiar, Michal Daniška, Roman Krčmár, Tomotoshi Nishino

  Jul. 2014, Physical Review E, 90(1) (1), 012122, English

  [Refereed]

  Scientific journal


• Doubling of entanglement spectrum in tensor renormalization group

  Hiroshi Ueda, Kouichi Okunishi, Tomotoshi Nishino

  Feb. 2014, Physical Review B, 89(7) (7), 075116, English

  [Refereed]

  Scientific journal


• Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices

  Andrej Gendiar, Roman Krcmar, Sabine Andergassen, Michal Daniška, Tomotoshi Nishino

  Aug. 2012, Physical Review E, 86(2) (2), 021105, English

  [Refereed]

  Scientific journal


• Boundary Condition, Topology and Energy-Scale Deformation in Quantum Systems

  Hikihara Toshiya, Katsura Hosho, Maruyama Isao, Nishino Tomotoshi

  Boundary condition and topology play a crucial role in determining the properties of quantum system. We report our recent finding that one can change the topology of the ground states of quantum critical systems by applying "sine-square deformation" which introduces a gradual modulation in local energy scale of the system but does not change the topology of the Hamiltonian. Implications of the result to several topics are also discussed.

  The Physical Society of Japan (JPS), Jun. 2012, 日本物理学会誌, 67(6) (6), 394 - 398, Japanese

  [Refereed]

  Scientific journal


• Hyperbolic Deformation Applied to S = 1 Spin Chains – Scaling Relation in Excitation Energy –

  Hiroshi Ueda, Hiroki Nakano, Koichi Kusakabe, Tomotoshi Nishino

  Sep. 2011, Journal of the Physical Society of Japan, 80(9) (9), 094001 - 094001, English

  [Refereed]

  Scientific journal


• Suppression of finite-size effects in one-dimensional correlated systems

  A. Gendiar, M. Daniška, Y. Lee, T. Nishino

  May 2011, Physical Review A, 83(5) (5), 052118, English

  [Refereed]

  Scientific journal


• Connecting distant ends of one-dimensional critical systems by a sine-square deformation

  Toshiya Hikihara, Tomotoshi Nishino

  American Physical Society (APS), Feb. 2011, Physical Review B, 83(6) (6), 060414(R), English

  [Refereed]

  Scientific journal


• Scale free property of Wilson's numerical renormalization group(New Development of Numerical Simulations in Low-Dimensional Quantum Systems: From Density Matrix Renormalization Group to Tensor Network Formulations) :

  Okunishi Kouichi, Nishino Tomotoshi

  物性研究刊行会, 2011, 物性研究, 95(6) (6), 621 - 621, English


• Wave Function Prediction : a Classical Background(New Development of Numerical Simulations in Low-Dimensional Quantum Systems: From Density Matrix Renormalization Group to Tensor Network Formulations) :

  NISHINO Tomotoshi

  物性研究刊行会, 2011, 物性研究, 95(6) (6), 628 - 628, English


• Analysis of 2D Hyperbolic Surfaces by Corner Transfer Matrix Renormalization Group(New Development of Numerical Simulations in Low-Dimensional Quantum Systems: From Density Matrix Renormalization Group to Tensor Network Formulations) :

  Gendiar Andrej, Nishino Tomotoshi

  物性研究刊行会, 2011, 物性研究, 95(6) (6), 632 - 632, English


• Phase Transition of the Ising Model on a Hyperbolic Lattice

  Takatsugu Iharagi, Andrej Gendiar, Hiroshi Ueda, Tomotoshi Nishino

  Oct. 2010, Journal of the Physical Society of Japan, 79(10) (10), 104001 - 104001, English

  [Refereed]

  Scientific journal


• Scale-free property and edge state of Wilson’s numerical renormalization group

  Kouichi Okunishi, Tomotoshi Nishino

  Oct. 2010, Physical Review B, 82(14) (14), 144409, English

  [Refereed]

  Scientific journal


• Interference Pattern between Flat Glasses

  NISHINO Tomotoshi, SHIRAI Nobu

  The Physical Society of Japan (JPS), Sep. 2010, 日本物理学会誌, 65(9) (9), 733 - 733, Japanese

  [Refereed]


• Scaling Relation for Excitation Energy under Hyperbolic Deformation

  H. Ueda, H. Nakano, K. Kusakabe, T. Nishino

  Sep. 2010, Progress of Theoretical Physics, 124(3) (3), 389 - 398, English

  [Refereed]

  Scientific journal


• A Classical Background for the Wave Function Prediction in the Infinite System Density Matrix Renormalization Group Method

  Hiroshi Ueda, Andrej Gendiar, Tomotoshi Nishino

  Physical Society of Japan, Mar. 2010, Journal of the Physical Society of Japan, 79(4) (4), 044001 - 044001, English

  [Refereed]

  Scientific journal


• Spherical Deformation for One-Dimensional Quantum Systems

  A. Gendiar, R. Krcmar, T. Nishino

  Oxford University Press (OUP), Feb. 2010, Progress of Theoretical Physics, 123(2) (2), 393 - 393, English

  [Refereed]

  Scientific journal


• 双曲平面上の古典格子模型と 1 次元量子系と 1 粒子量子力学

  西野友年, 上田宏, Andrej Gendiar

  京都大学, 2010, 数理解析研究所講究録, 1705, 237 - 240, Japanese

  Research institution


• Spherical Deformation for One-Dimensional Quantum Systems

  A. Gendiar, R. Krcmar, T. Nishino

  Oct. 2009, Progress of Theoretical Physics, 122(4) (4), 953 - 967, English

  [Refereed]

  Scientific journal


• Hyperbolic Deformation on Quantum Lattice Hamiltonians

  Hiroshi Ueda, Tomotoshi Nishino

  A group of non-uniform quantum lattice Hamiltonians in one dimension is introduced, which is related to the hyperbolic ($1 + 1$)-dimensional space. The Hamiltonians contain only nearest neighbor interactions whose strength is proportional to $\cosh j \lambda$, where $ j$ is the lattice index and where $\lambda \geq 0$ is a deformation parameter. In the limit $\lambda \rightarrow 0$ the Hamiltonians become uniform. Spacial translation of the deformed Hamiltonians is induced by the corner Hamiltonians. As a simple example, we investigate the ground state of the deformed $S = 1/2$ Heisenberg spin chain by use of the density matrix renormalization group (DMRG) method. It is shown that the ground state is dimerized when $\lambda$ is finite. Spin correlation function show exponential decay, and the boundary effect decreases with increasing $\lambda$.

  Physical Society of Japan, Jan. 2009, Journal of the Physical Society of Japan, 78(1) (1), 014001 - 014001, English

  [Refereed]

  Scientific journal


• 繰り込みか?それとも変分か? : 双曲変形という考え方(京都大学基礎物理学研究所研究会 密度行列繰り込み群法を用いた物性研究の新展開,研究会報告)[In Japanese]

  Tomotoshi Nishino, Hiroshi Ueda

  この論文は国立情報学研究所の電子図書館事業により電子化されました。研究会報告

  物性研究刊行会, 2009, Butsuri, 91(6) (6), 739 - 739, Japanese

  Symposium


• Tricritical point of the J1−J2 Ising model on a hyperbolic lattice

  R. Krcmar, T. Iharagi, A. Gendiar, T. Nishino

  Dec. 2008, Physical Review E, 78(6) (6), 061119, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Two-Site Shift Product Wave Function Renormalization Group Method Applied to Quantum Systems

  Hiroshi Ueda, Tomotoshi Nishino, Koichi Kusakabe

  Nov. 2008, Journal of the Physical Society of Japan, 77(11) (11), 114002 - 114002

  [Refereed]

  Scientific journal


• Phase transition of clock models on a hyperbolic lattice studied by corner transfer matrix renormalization group method

  A. Gendiar, R. Krcmar, K. Ueda, T. Nishino

  Apr. 2008, Physical Review E, 77(4) (4), 041123, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Ising model on a hyperbolic lattice studied by the corner transfer matrix renormalization group method

  R Krcmar, A Gendiar, K Ueda, T Nishino

  IOP Publishing, Mar. 2008, Journal of Physics A: Mathematical and Theoretical, 41(12) (12), 125001 - 125001, English

  [Refereed]

  Scientific journal


• 双曲平面上のイジング模型が示す臨界現象

  西野 友年, 上田 幸治, Roman Krcmar, Andrej Gendiar

  京都大学, 2008, 数理解析研研究会講究録, 1600, 185 - 191, Japanese

  Research institution


• Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane

  Kouji Ueda, Roman Krcmar, Andrej Gendiar, Tomotoshi Nishino

  Aug. 2007, Journal of the Physical Society of Japan, 76(8) (8), 084004 - 084004, English

  [Refereed]

  Scientific journal


• Modulation of Local Magnetization in Two-Dimensional Axial-Next-Nearest-Neighbor Ising Model

  René Derian, Andrej Gendiar, Tomotoshi Nishino

  Physical Society of Japan, Nov. 2006, Journal of the Physical Society of Japan, 75(11) (11), 114001 - 114001, English

  [Refereed]

  Scientific journal


• Product Wave Function Renormalization Group: Construction from the Matrix Product Point of View

  Kouji Ueda, Tomotoshi Nishino, Kouichi Okunishi, Yasuhiro Hieida, Rene Derian, Andrej Gendiar

  Jan. 2006, Journal of the Physical Society of Japan, 75(1) (1), 014003 - 014003, English

  [Refereed]

  Scientific journal


• Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix RG

  Nishino T., Ueda K., Otani R.

  Kyoto University, 2006, RIMS Kokyuroku, 1482, 180 - 190, Japanese

  Research institution


• 角転送行列繰り込み群による古典スピン系のスナップショット生成 (モンテカルロ法の新展開(3))

  上田 幸治, 大谷 両太, 西尾 幸暢, Gendiar Andrej, 西野 友年

  この論文は国立情報学研究所の電子図書館事業により電子化されました。

  物性研究刊行会, Dec. 2005, 物性研究, 85(3) (3), 388 - 392, Japanese


• Critical Point of a Symmetric Vertex Model

  Kouji Ueda, Ryota Otani, Yukinobu Nishio, Andrej Gendiar, Tomotoshi Nishino

  Jun. 2005, Journal of the Physical Society of Japan, 74(6) (6), 1871 - 1872, English

  [Refereed]

  Scientific journal


• Phase diagram of the three-dimensional axial next-nearest-neighbor Ising model

  A. Gendiar, T. Nishino

  American Physical Society (APS), Jan. 2005, Physical Review B, 71(2) (2), 024404[7ages], English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• 二次元量子スピン系のテンソル積変分法による解析(2004年度後期基礎物理学研究所研究会「モンテカルロ法の新展開3」,研究会報告)

  西尾 幸暢, Gendiar Andrej, 西野 友年

  物性研究刊行会, 2005, 物性研究, 85(3) (3), 399 - 403, Japanese


• Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group

  Kouji Ueda, Ryota Otani, Yukinobu Nishio, Andrej Gendiar, Tomotoshi Nishino

  Jan. 2005, Journal of the Physical Society of Japan, 74(Suppl) (Suppl), 111 - 114, English

  [Refereed]

  Scientific journal


• 密度行列繰り込み群と幾つかの変分原理

  西野 友年

  京都大学, 2004, 数理解析研究所講究録出版, 1386, 117 - 131, Japanese

  Research institution


• Stable Optimization of a Tensor Product Variational State

  A. Gendiar, N. Maeshima, T. Nishino

  Oct. 2003, Progress of Theoretical Physics, 110(4) (4), 691 - 699, English

  [Refereed]

  Scientific journal


• 2次元量子スピン系基底状態のテンソル積変分による評価 (〔基研研究会〕新奇な秩序を持つ系での相転移)

  西野 友年

  この論文は国立情報学研究所の電子図書館事業により電子化されました。

  物性研究刊行会, Feb. 2003, 物性研究, 79(5) (5), 837 - 839, Japanese


• Stochastic light-cone CTMRG: a new DMRG approach to stochastic models

  A Kemper, A Gendiar, T Nishino, A Schadschneider, J Zittartz

  IOP Publishing, Jan. 2003, Journal of Physics A: Mathematical and General, 36(1) (1), 29 - 41, English

  [Refereed]

  Scientific journal


• Latent heat calculation of the three-dimensionalq=3,4, and 5 Potts models by the tensor product variational approach

  A. Gendiar, T. Nishino

  American Physical Society (APS), Apr. 2002, Physical Review E, 65(4) (4), 046702[7ages], English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Matrix Product State Approximation for the Maximum-Eigenvalue Eigenstate of the Quantum Transfer Matrix

  Nobuya Maeshima, Yasuhiro Hieida, Tomotoshi Nishino, Kouichi Okunishi

  We propose a matrix product state (MPS) formulation to calculate thermodynamic quantities of one dimensional (1D) quantum systems. The maximum-eigenvalue eigenstate of the quantum transfer matrix is represented as the product of local matrices, which are obtained by the DMRG method for the two dimensional (2D) classical system mapped from the original 1D quantum system. This MPS formulation is successfully applied to the S = 1/2 XY model.

  Oxford University Press (OUP), 2002, Progress of Theoretical Physics Supplement, 145(145) (145), 204 - 207, English

  [Refereed]

  Scientific journal


• 密度行列繰り込み群

  西野友年

  2002, 数理解析研究所講究録, 1275, 182 - 192

  Research institution


• Interaction-round-a-face density-matrix renormalization-group method

  Tatsuaki Wada, Tomotoshi Nishino

  Elsevier BV, Dec. 2001, Computer Physics Communications, 142(1-3) (1-3), 164 - 167, English

  [Refereed]

  Scientific journal


• Vertical density matrix algorithm: A higher-dimensional numerical renormalization scheme based on the tensor product state ansatz

  Nobuya Maeshima, Yasuhiro Hieida, Yasuhiro Akutsu, Tomotoshi Nishino, Kouichi Okunishi

  American Physical Society (APS), Jun. 2001, Physical Review E, 64(1) (1), 016705[6ages], English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Phase Diagram of a 2D Vertex Model

  Hiroshi Takasaki, Tomotoshi Nishino, Yasuhiro Hieida

  Physical Society of Japan, May 2001, Journal of the Physical Society of Japan, 70(5) (5), 1429 - 1430, English

  [Refereed]

  Scientific journal


• Two-Dimensional Tensor Product Variational Formulation

  T. Nishino, Y. Hieida, K. Okunishi, N. Maeshima, Y. Akutsu, A. Gendiar

  We propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as a two-dimensional product of tensors. The variational partition function is calculated using the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The numerical efficiency of the method is exemplified in its application to the 3D Ising model.

  Oxford University Press (OUP), Mar. 2001, Progress of Theoretical Physics, 105(3) (3), 409 - 417, English

  [Refereed]

  Scientific journal


• Self-consistent tensor product variational approximation for 3D classical models

  T. Nishino, K. Okunishi, Y. Hieida, N. Maeshima, Y. Akutsu

  Elsevier BV, Jun. 2000, Nuclear Physics B, 575(3) (3), 504 - 512, English

  Scientific journal


• 密度行列繰り込み群

  西野 友年, 日永田 泰啓, 奥西 巧一

  May 2000, 日本物理学会誌, 55(10) (10), 763 - 771, Japanese

  [Refereed]

  Scientific journal


• Ground-State Phase Diagram of the Spin-\(\frac{\bf 1},{\bf 2}\)-\(\frac{\bf 1},{\bf 2}\)-1-1 Chain

  Toshiya Hikihara, Takashi Tonegawa, Makoto Kaburagi, Tomotoshi Nishino, Seiji Miyashita, Hans-Jürgen Mikeska

  We investigate the ground-state phase diagram of the quantum mixed spin chainin which two $S\!=\!\frac{1},{2}$ and two S=1 spins arearranged alternatively and isotropic exchange interactions betweennearest-neighboring pairs of spins are assumed. Guided by our previousresults [J. Phys. Soc. Jpn. 67 (1998) 1000] for a few limiting cases ofthe exchange interactions, we carry out a density-matrix renormalization-groupcalculation to determine the ground-state phase diagram in detail. From thegapless points of the singlet-triplet energy gap, five boundary lines aredetermined, which divide the phase diagram into six regions. In three regionsthe ground states with the Haldane-phase character appear, while in theremaining three regions those with the dimer character appear. We alsopresent a characterization of the phases concerning how the ground state ineach phase is represented in the framework of the valence-bond-solid (VBS)picture. Making use of the matrix-product wave function, we classify the VBSpictures and interpret the ground-state phase diagram in terms of symmetriesschematically related to the VBS pictures. We investigate the ground-statenearest-neighboring two-spin correlation functions and a kind of string orderparameters, by which we confirm the validity of the characterization.

  Physical Society of Japan, Apr. 2000, Journal of the Physical Society of Japan, 69(4) (4), 1207 - 1218, English

  [Refereed]

  Scientific journal


• Kramers-Wannier Approximation for the 3D Ising Model

  K. Okunishi, T. Nishino

  We investigate the Kramers-Wannier approximation for the three-dimensional (3D) Ising model. The variational state is represented by an effective 2D Ising model, which contains two variational parameters. We numerically calculate the variational partition function using the corner transfer matrix renormalization group (CTMRG) method, and find its maximum with respect to the variational parameters. The value of the calculated transition point, K_c = 0.2184 , is only 1.5 % less than the true K_c. This result is better than that obtained using the corner transfer tensor renormalization group (CTTRG) approach. The calculated phase transition is mean-field like.

  Oxford University Press (OUP), Mar. 2000, Progress of Theoretical Physics, 103(3) (3), 541 - 548, English

  [Refereed]

  Scientific journal


• Estimation of the magnetic critical exponent by Tensor Product Variational Approach

  Andrej Gendiar, Tomotoshi Nishino, Rene Derian

  2000, Acta Physica Slovaca, 55(2) (2), 141 - 148, English

  [Refereed]


• Efficiency of Asymmetric Targeting for Finite-TDMRG

  Tomotoshi Nishino, Naokazu Shibata

  Two targeting schemes have been known for the density matrixrenormalization group (DMRG) applied to non-Hermitian problems; one usesan asymmetric density matrix and the other uses symmetric densitymatrix. We compare the numerical efficiency of these two targetingschemes when they are used for the finite temperature DMRG.

  Physical Society of Japan, Nov. 1999, Journal of the Physical Society of Japan, 68(11) (11), 3501 - 3504, English

  [Refereed]

  Scientific journal


• Fixed Point of the Finite System DMRG

  Hiroshi Takasaki, Toshiya Hikihara, Tomotoshi Nishino

  The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system algorithm, that uses the block structure B •• B.This is because the tensors are not improved directly. We overcomethis problem by using the simpler block structure B • Bfor the final several sweeps in the finite iteration process. It is possible toincrease the numerical precision of the finite system algorithm without increasing the computational effort.

  Physical Society of Japan, May 1999, Journal of the Physical Society of Japan, 68(5) (5), 1537 - 1540, English

  [Refereed]

  Scientific journal


• Spin, Charge and Quasi-Particle Gaps in the One-Dimensional Kondo Lattice withf2Configuration

  Shinji Watanabe, Yoshio Kuramoto, Tomotoshi Nishino, Naokazu Shibata

  The ground state properties of the one-dimensional Kondo latticewith an f2 configuration at each siteare studied by the density matrix renormalization group method.At half-filling, competition between the Kondo exchange J and the antiferromagnetic intra f-shell exchange I leads to reduction of energy gaps for spin, quasi-particle and charge excitations. The attractive force among conduction electrons is induced by the competition and the bound state is formed. As J/I increases the f2 singlet gives way to the Kondo singlet as the dominant local correlation.The remarkable change of the quasi-particle gap is driven by the change of the spin-1/2 excitation character from the itinerant one to the localized one. Possible metal-insulator transition is discussed which may occur asthe ratio J/I is varied by reference to mean-field results in the f2 lattice system and the two impurity Kondo system.

  Physical Society of Japan, Jan. 1999, Journal of the Physical Society of Japan, 68(1) (1), 159 - 165, English

  [Refereed]

  Scientific journal


• DENSITY MATRIX RENORMALIZATION GROUP: INTRODUCTION FROM A VARIATIONAL POINT OF VIEW

  T. NISHINO, T. HIKIHARA, K. OKUNISHI, Y. HIEIDA

  The density matrix renormalization group theory is reviewed as a numerical variational method. The variational state, expressed as a product of local tensors, is improved through locally tuning each tensor. The first section is a tutorial with simplified discussions. Details are discussed in the subsequent sections. The review concludes with some recent developments and future directions.

  World Scientific Pub Co Pte Lt, Jan. 1999, International Journal of Modern Physics B, 13(01) (01), 1 - 24, English

  [Refereed]

  Scientific journal


• Ground State and Elementary Excitation Gaps in the One-Dimensional Kondo Lattice with f^2 Configuration :

  WATANABE Shinji, KURAMOTO Yoshio, NISHINO Tomotoshi, SHIBATA Naokazu

  Japanese Journal of Applied Physics, 1999, JJAP series, 11, 106 - 108, English


• Transfer-matrix approach to classical systems

  T. Nishino, K. Okunishi, Y. Hieida, T. Hikihara, H. Takasaki

  Springer Berlin Heidelberg, 1999, Density-Matrix Renormalization, 127 - 148, English

  [Refereed]

  In book


• A Density Matrix Algorithm for 3D Classical Models

  Tomotoshi Nishino, Kouichi Okunishi

  We generalize the corner transfer matrix renormalization group, whichconsists of White's density matrix algorithm and Baxter'smethod of the corner transfer matrix, to three dimensional (3D) classicalmodels. The renormalization group transformation is obtained through the diagonalization of density matrices for a cubic cluster.A trial application to 3D Ising model with m = 2 is shown as thesimplest case.

  Physical Society of Japan, Sep. 1998, Journal of the Physical Society of Japan, 67(9) (9), 3066 - 3072, English

  [Refereed]

  Scientific journal


• Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains

  J Dukelsky, M. A Martín-Delgado, T Nishino, G Sierra

  IOP Publishing, Aug. 1998, Europhysics Letters (EPL), 43(4) (4), 457 - 462, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• DMRG 学習にお勧めの文献

  西野友年

  「密度行列繰り込み群(DMRG)[1]を学び、これを使いこなして研究を進めようと思い立った方々にお勧めの文献は何ですか?」と聞かれると、しばらく返答につまります。何よりもまずWhiteによる本論文[2]をお勧めしたいのですがヽこれは解説記事ではないので、[3]読みこなす為には多少の"数値計算の心得"が必要だからです。そういう訳でDMRG学習の副読本を探してみました。これから、幾つか文献を挙げて行きますが、とりわけお勧めなのが最初に挙げる成島毅氏の修士論文です。[4]和文の丁寧な解説としては、今の所これに替わり得る物はありません。幸いなことに、成島氏の論文はこの記事の直後に全文掲載されていますので、ぜひ御覧になって下さい。

  物性研究刊行会, May 1998, 物性研究, 69(5) (5), 697 - 701, Japanese

  Research institution


• Numerical Latent Heat Observation of theq=5Potts Model

  Tomotoshi Nishino, Kouichi Okunishi

  Physical Society of Japan, Apr. 1998, Journal of the Physical Society of Japan, 67(4) (4), 1492 - 1493, English

  [Refereed]

  Scientific journal


• Ground-State and Thermodynamic Properties of the Quantum Mixed Spin-1/2-1/2-1-1 Chain

  Takashi Tonegawa, Toshiya Hikihara, Makoto Kaburagi, Tomotoshi Nishino, Seiji Miyashita, Hans-Jürgen Mikeska

  We investigate both analytically and numerically the ground-state andthermodynamic properties of the quantum mixed spin-1/2-1/2-1-1chain described by the Hamiltonian ${\cal H}\!=\!\sum_{\ell=1}^{N/4}\bigl(J_1\,{\vec s}_{4\ell-3}\cdot{\vec s}_{4\ell-2}\!+\!J_2\,{\vec s}_{4\ell-2}\cdot {\vec S}_{4\ell-1}\!+\!J_3\, {\vec S}_{4\ell-1}\cdot {\vec S}_{4\ell}\!+\!J_2\, {\vec S}_{4\ell}\cdot{\vec s}_{4\ell+1}\bigr)$, where two S=1/2 spins(${\vec s}_{4\ell-3}$ and ${\vec s}_{4\ell-2}$) and two S=1 spins($ {\vec S}_{4\ell-1}$ and $ {\vec S}_{4\ell}$) are arranged alternatively. Inseveral limiting cases of J1, J2, and J3 we apply the Wigner-Eckarttheorem and carry out a perturbation calculation to examine the behavior ofthe massless lines where the energy gap vanishes. Performing a quantum MonteCarlo calculation without global flips at a sufficiently low temperature forthe case where J1=J3=1.0 and J2>0, we find that theground state of the present system in this case undergoes a second-order phasetransition accompanying the vanishing of the energy gap atJ2=J2 c with J2 c=0.77±0.01. We alsofind that the ground states for both J2J2 c can be understood by means of thevalence-bond-solid picture. A quantum Monte Carlo calculation which takes theglobal flips along the Trotter direction into account is carried out toelucidate the temperature dependences of the specific heat and the magneticsusceptibility. In particular, it is found that the susceptibility per unitcell for J2=0.77 with J1=J3=1.0 takes a finite value atabsolute zero temperature and that the specific heat per unit cell versustemperature curve for J2=5.0 with J1=J3=1.0 has a doublepeak.

  Physical Society of Japan, Mar. 1998, Journal of the Physical Society of Japan, 67(3) (3), 1000 - 1013, English

  [Refereed]

  Scientific journal


• One-dimensional Heisenberg antiferromagnet in which two S = ½ and two S = 1 spins are arranged alternatively

  T. Tonegawa, T. Hikihara, T. Nishino, M. Kaburagi, S. Miyashita, H.-J. Mikeska

  Elsevier BV, Jan. 1998, Journal of Magnetism and Magnetic Materials, 177-181, 647 - 649, English

  [Refereed]

  Scientific journal


• Corner Transfer Matrix Algorithm for Classical Renormalization Group

  Tomotoshi Nishino, Kouichi Okunishi

  We report a real-space renormalization group (RSRG) algorithm, whichis formulated through Baxter's corner transfer matrix (CTM), fortwo-dimensional (d = 2) classical lattice models. The new methodperforms the renormalization group transformation according to White'sdensity matrix algorithm, so that variational free energies are minimizedwithin a restricted degree of freedom. As a consequence of therenormalization, spin variables on each corner of CTM are replaced by am-state block spin variable. It is shown that the thermodynamic functionsand critical exponents of the q = 2, 3 Potts models can be preciselyevaluated by use of the renormalization group method.

  Physical Society of Japan, Oct. 1997, Journal of the Physical Society of Japan, 66(10) (10), 3040 - 3047, English

  [Refereed]

  Scientific journal


• The density matrix renormalization group method applied to interaction round a face Hamiltonians

  Germán Sierra, Tomotoshi Nishino

  Elsevier BV, Jun. 1997, Nuclear Physics B, 495(3) (3), 505 - 532, English

  [Refereed]

  Scientific journal


• Large Fermi surface of the one-dimensional Kondo lattice model observed by Friedel oscillations

  Naokazu Shibata, Kazuo Ueda, Tomotoshi Nishino, Chikara Ishii

  Elsevier BV, Feb. 1997, Physica B: Condensed Matter, 230-232, 1024 - 1027, English

  [Refereed]

  Scientific journal


• 「密度行列繰り込み群」の変分原理

  西野, 友年, 奥西, 巧一, 引原, 俊哉

  密度行列繰り込み群(DMRG)の正体は、「密度行列より導かれる精密な数値変分法」です。変分法というと、「基底波動関数の形を物理的直感に基づいて独断と偏見で定める」ような職人芸的な方法…に聞こえますが、DMRGは「計算対象に最適な変分関数を自動生成する」という点で従来の数値変分法とは一線を画しています。この解説記事では、DMRGの細かな計算手続きよりも、その基本原理に目を向けることにします。「密度行列」繰り込み群という名前の由来や、DMRGの背後にある変分原理について、一緒に考えましょう。

  物性研究刊行会, Feb. 1997, 物性研究, 68(2) (2), 133 - 155, Japanese

  Research institution


• Density matrix and renormalization for classical lattice models

  T. Nishino, K. Okunishi

  Springer Berlin Heidelberg, 1997, Strongly Correlated Magnetic and Superconducting Systems, 167 - 183, English

  [Refereed]

  In book


• Origin of Magic Angular Momentum in a Quantum Dot under Strong Magnetic Field

  Taku Seki, Yoshio Kuramoto, Tomotoshi Nishino

  This paper investigates origin of the extra stability associated with particular values (magic numbers) of the total angular momentum of electrons in a quantum dot under strong magnetic field.The ground-state energy, distribution functions of density and angular momentum, and pair correlation function are calculated in the strong field limit by numerical diagonalization of the system containing up to seven electrons.It is shown that the composite fermion picture explains the small magic numbers well, while a simple geometrical picture does better as the magic number increases.Combination of these two pictures leads to identification of all the magic numbers. Relation of the magic-number states to the Wigner crystal and the fractional quantum Hall state is discussed.

  Physical Society of Japan, Dec. 1996, Journal of the Physical Society of Japan, 65(12) (12), 3945 - 3951, English

  [Refereed]

  Scientific journal


• Friedel oscillations in the one-dimensional Kondo lattice model

  Naokazu Shibata, Kazuo Ueda, Tomotoshi Nishino, Chikara Ishii

  American Physical Society (APS), Nov. 1996, Physical Review B, 54(19) (19), 13495 - 13498, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• IMPURITY BOND EFFECT ON THE ANTIFERROMAGNETIC ISING-LIKE CHAIN

  MAKOTO KABURAGI, TAKAO MORIWAKI, TOMOTOSHI NISHINO, TAKASHI TONEGAWA

  We investigate the effect of an impurity bond on low-lying excited states of the antiferromagnetic Ising-like chain in terms of domain-wall excitations, using an analytical method and a numerical method. The fundamental difference between the chains with even and odd numbers of spins is discussed.

  World Scientific Pub Co Pte Lt, Jun. 1996, International Journal of Modern Physics C, 07(03) (03), 457 - 462, English

  [Refereed]

  Scientific journal


• Corner Transfer Matrix Renormalization Group Method

  Tomotoshi Nishino, Kouichi Okunishi

  We propose a new fast numerical renormalization group method —the corner transfer matrix renormalization group (CTMRG) method —which is based on a unified scheme involving Baxter's corner transfermatrix method and White's density matrix renormalization groupmethod. The key point is that a product of four corner transfermatrices coincides with the density matrix. We formulate CTMRG as a renormalization group for 2D classical models.

  Physical Society of Japan, Apr. 1996, Journal of the Physical Society of Japan, 65(4) (4), 891 - 894, English

  [Refereed]

  Scientific journal


• Numerical renormalization group at criticality

  T. Nishino, K. Okunishi, M. Kikuchi

  Elsevier BV, Apr. 1996, Physics Letters A, 213(1-2) (1-2), 69 - 72, English

  [Refereed]

  Scientific journal


• Spin and charge gaps in the one-dimensional Kondo-lattice model with Coulomb interaction between conduction electrons

  Naokazu Shibata, Tomotoshi Nishino, Kazuo Ueda, Chikara Ishii

  American Physical Society (APS), Apr. 1996, Physical Review B, 53(14) (14), R8828 - R8831, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Gap-formation mechanism of the Kondo-necklace model

  Hiromi Otsuka, Tomotoshi Nishino

  American Physical Society (APS), Dec. 1995, Physical Review B, 52(21) (21), 15066 - 15069, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Product Wave Function Renormalization Group

  Tomotoshi Nishino, Kouichi Okunishi

  We propose a fast numerical renormalization group method-the productwave function renormalization group (PWFRG) method-for 1D quantumlattice models and 2D classical ones. A variational wave function,which is expressed as a matrix product, is improved through aself-consistent calculation. The new method has the same fixed pointas the density matrix renormalization group method.

  Physical Society of Japan, Nov. 1995, Journal of the Physical Society of Japan, 64(11) (11), 4084 - 4087, English

  [Refereed]

  Scientific journal


• Density Matrix Renormalization Group Method for 2D Classical Models

  Tomotoshi Nishino

  The density matrix renormalization group (DMRG) method isapplied to the interaction round a face (IRF) model. When thetransfer matrix is asymmetric, singular-value decompositionof the density matrix is required. A trial numericalcalculation is performed on the square lattice Ising model,which is a special case of the IRF model.

  Physical Society of Japan, Oct. 1995, Journal of the Physical Society of Japan, 64(10) (10), 3598 - 3601, English

  [Refereed]

  Scientific journal


• Dynamical correlation functions of one-dimensional Kondo insulators

  Tomotoshi Nishino, Kazuo Ueda

  Elsevier BV, Feb. 1995, Physica B: Condensed Matter, 206-207, 813 - 815, English

  [Refereed]

  Scientific journal


• Large Fermi surface of the one-dimensional Kondo lattice model

  Kazuo Ueda, Tomotoshi Nishino, Hirokazu Tsunetsugu

  American Physical Society (APS), Jul. 1994, Physical Review B, 50(1) (1), 612 - 615, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• The groundstate phase diagram of the Kondo lattice model

  Kazuo Ueda, Manfred Sigrist, Hirokazu Tsunetsugu, Tomotoshi Nishino

  Elsevier BV, Feb. 1994, Physica B: Condensed Matter, 194-196, 255 - 256, English

  [Refereed]

  Scientific journal


• Fermi Volume of the Kondo-Lattice Model

  T. Nishino, K. Ueda, H. Tsunetsugu

  Springer Berlin Heidelberg, 1994, Correlation Effects in Low-Dimensional Electron Systems, 113 - 120, English

  [Refereed]

  In book


• Spin- and charge-excitation gaps in the one-dimensional periodic Anderson model

  T. Nishino, Kazuo Ueda

  American Physical Society (APS), May 1993, Physical Review B, 47(19) (19), 12451 - 12458, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Survey of the charge excitation gap by a 2D filter

  T. Nishino

  Elsevier BV, May 1993, Physica B: Condensed Matter, 186-188, 885 - 887, English

  [Refereed]

  Scientific journal


• Charge Excitation Gap of the Extended Hubbard Model*

  Tomotoshi Nishino

  The author investigates the one-dimensional extended Hubbard model, i.e. the Hubbard model with additional nearest neighbor Coulomb repulsion $V$. The charge excitation gap at half-filling is obtained numerically. The calculated gap is smaller than that given by the Hartree-Fock approximation, especially near the phase boundary. The gap is finite at the boundary when $U{=}12$, the result which gives an upper bound for the position of the tricritical point.

  Physical Society of Japan, Oct. 1992, Journal of the Physical Society of Japan, 61(10) (10), 3651 - 3657, English

  [Refereed]

  Scientific journal


• Numerical Study of Quantum Spin Systems

  M. Kaburagi, T. Tonegawa, T. Nishino

  Springer Berlin Heidelberg, 1992, Springer Proceedings in Physics, 179 - 180, English

  [Refereed]

  In book


• Ground State Wave Function of an Extended Hubbard Model

  T. Nishino

  Springer Berlin Heidelberg, 1992, Springer Proceedings in Physics, 70, 117 - 118, English

  In book


• Internal Magnetic Field at the La Atom in La2MO4(M=Cu, Ni)

  Manabu Takahashi, Tomotoshi Nishino, Junjiro Kanamori

  A cluster model calculation in which a tight binding Hamiltonian including intraatomic electron electron interaction is exactly diagonalized is carried out to explain the observed values of the internal magnetic fields at the La site in La2CuO4 and La2NiO4 which are about 1 kOe and about 18 kOe, respectively. It is shown that the internal fields reflect the spin correlation between apical oxygen and Cu or Ni, and that the electron correlation is important to determine the magnitude of the field.

  Physical Society of Japan, Apr. 1991, Journal of the Physical Society of Japan, 60(4) (4), 1365 - 1371, English

  [Refereed]

  Scientific journal


• Effect of Hole Itinerancy on XAS and XPS Spectra of the High-TcCompounds

  Tomotoshi Nishino

  Spectra of Cu 2$p$ XPS, XAS, valence band XPS and BIS of the high-$T_{\text{c } }$ compounds are calculated for CunOm ($n{>}1$) clusters. Effects of the hole itinerancy as well as those of the hole correlation on these spectra are investigated. Size dependence of the spectra including the valence band XPS and BIS as well is examined by extending the calculation to linear clusters containing up to seven Cu atoms. It is concluded that the Cu 2$p$ XPS spectra consist generally of three groups of peaks which are assigned to $|\underline{c}d^{10}\underline{L}\rangle$, $|\underline{c}d^{9}\rangle$ and $|\underline{c}d^{10}\underline{L}^{2}\rangle$ final states. The last one which was not obtained by use of either a single Cu atom cluster or the impurity Anderson model appears in between the first two in energy. The main peak corresponding to the $|\underline{c}d^{10}\underline{L}\rangle$ state shifts with concentration of additional holes consistently with experimental data on Y–Ba–Cu oxides.

  Physical Society of Japan, Dec. 1990, Journal of the Physical Society of Japan, 59(12) (12), 4376 - 4383, English

  [Refereed]

  Scientific journal


• Electronic Structure of Cu-O3Pyramidal Plane -Effect of Hole Itinerancy-

  Tomotoshi Nishino, Junjiro Kanamori

  The electronic structure of the CuO2 plane with apex oxygens is investigated by calculating the ground state wave function of a Cu4O12 cluster with the periodic boundary condition for two in-plane directions. The cluster is the smallest among those taking account of the electron transfer between CuO5 units with the translational invariance of the CuO2 plane. When extra holes are introduced, they have amplitudes on all the atoms including the apex oxygens unlike the case of a single CuO5 cluster. No appreciable spin correlation between the apex oxygen $p_{z}$ orbital and Cu $d(x^{2}-y^{2})$ is found. Spin correlations between other pairs of orbitals and spin and charge fluctuations of a CuO5 cluster are also examined.

  Physical Society of Japan, Jan. 1990, Journal of the Physical Society of Japan, 59(1) (1), 253 - 258, English

  [Refereed]

  Scientific journal


• 10. Pairing Mechanism of Holes in High Tc Superconductors : Attraction through spin polarization in the Cu-O plane :

  西野 友年

  この論文は国立情報学研究所の電子図書館事業により電子化されました。

  物性研究刊行会, 1989, 物性研究, 53(1) (1), 125 - 126, English


• A model for superconducting Cu oxides: The oxygen p band hybridized with d(3z2-r2) of Cu

  Tomotoshi Nishino, Macoto Kikuchi, Junjiro Kanamori

  Elsevier BV, Nov. 1988, Solid State Communications, 68(5) (5), 455 - 458, English

  [Refereed]

  Scientific journal

• Network from Microscopic to Macroscopic

  Tomotoshi Nishino

  Jan. 2022, 数理科学, 60(2) (2), 5 - 6, Japanese

  Introduction commerce magazine


• 物理数学 (特集 大学数学のキーポイント(後篇))

  西野 友年

  日本評論社, May 2019, 数学セミナー, 58(5) (5), 42 - 46, Japanese


• Finite-m scaling of corner transfer matrix renormalization group for BKT transition

  Ueda Hiroshi, Okunishi Kouichi, Harada Kenji, Krcmar Roman, Gendiar Andrej, Yunoki Seiji, Nishino Tomotoshi

  The Physical Society of Japan, 2019, Meeting Abstracts of the Physical Society of Japan, 74.1, 2669 - 2669, Japanese


• Entanglement partitioning and mutual-information-entropy-optimization principle for TTN

  Okunishi Kouichi, Ueda Hiroshi, NIshino Tomotoshi

  The Physical Society of Japan, 2019, Meeting Abstracts of the Physical Society of Japan, 74.2, 2339 - 2339, Japanese


• Finite-m scaling of corner transfer matrix renormalization group for entanglement spectrum

  Ueda Hiroshi, Okunishi Kouichi, Yunoki Seiji, Nishino Tomotoshi

  The Physical Society of Japan, 2019, Meeting Abstracts of the Physical Society of Japan, 74.2, 2341 - 2341, Japanese


• 量子情報とテンソルネットワーク (特集 量子情報と物理学のフロンティア)

  西野 友年

  サイエンス社, Jun. 2018, 数理科学, 56(6) (6), 38 - 45, Japanese


• 量子論と統計力学 (特集 量子論的思考法のすすめ : 量子力学から見た諸分野の姿)

  西野 友年

  サイエンス社, Mar. 2018, 数理科学, 56(3) (3), 22 - 28, Japanese


• Phase transition of the Ising model on the Sierpinski carpet

  Nishino Tomotoshi, Genzor Jozef

  The Physical Society of Japan, 2018, Meeting Abstracts of the Physical Society of Japan, 73, 2348 - 2348, Japanese


• Phase diagram and critical property of the icosahedral model on the square lattice

  Ueda Hiroshi, Okunishi Kouichi, Krcmar Roman, Gendiar Andrej, Yunoki Seiji, Nishino Tomotoshi

  The Physical Society of Japan, 2017, Meeting Abstracts of the Physical Society of Japan, 72, 2585 - 2585, Japanese


• Phase transition of the 6-clock model on the square lattice, observed by means of the entanglement entropy.

  Nishino Tomotoshi, Krcmar Roman, Gendiar Andrej

  正方格子上の６状態クロック模型の BKT 転移を、角転送行列繰り込み群により数値的に観察し、臨界現象をエンタングルメント・エントロピーから解析した。得られた、エンタングルメント・エントロピーのグラフは、「天の香具山」を彷彿とさせる、のどかな曲線であった。主観はともかくとして、定量解析により、BKT 転移を外挿により推定した。

  The Physical Society of Japan, 2017, Meeting Abstracts of the Physical Society of Japan, 72, 2755 - 2755, Japanese


• From Matrix Product State to Tensor Network: Formulations and Developments

  Nishino Tomotoshi

  The Physical Society of Japan, 2017, Meeting Abstracts of the Physical Society of Japan, 72, 2889 - 2890, Japanese


• Entanglement Entropy of the +- J Ising Model

  Sasagawa Yoshinori, Nishino Tomotoshi

  有限サイズの2次元イジングモデルにおいて、最近接スピンの相互作用が +- Jのランダムな場合を考える。この系のエンタングルメント・エントロピーを、密度行列の特異値分解により数値的に求める。その振る舞いの温度依存性について報告する。また、このようなランダム系のモデルは情報処理の分野においても注目されており、ここでの考察を完全ランダム系への足がかりとしたい。

  The Physical Society of Japan, 2016, Meeting Abstracts of the Physical Society of Japan, 71, 2868 - 2868, Japanese


• Entanglement Entropy around a Hole on the Square-Lattice Ising Model

  Nishino Tomotoshi

  正方格子イジングモデルの有限サイズ系を考え、その中央に小さな「穴」がある場合を想定する。穴の周の一点から、系の外側の境界へ向けて直線を引くと、これに対応する密度行列を定義できる。規格化された密度行列の固有値から求められるエンタングルメント・エントロピーは、漸近的には穴の半径の対数に比例して増減するが、これに格子間隔から来る補正項が存在する可能性がある。これについて数値的に検証する。

  The Physical Society of Japan, 2016, Meeting Abstracts of the Physical Society of Japan, 71, 2722 - 2722, Japanese


• 19pBT-8 Phase Transition of the Ising Model on a Fractal Lattice by means of HOTRG method

  Nishino T., Genzor Jozef, Gendiar Andrej

  The Physical Society of Japan, 2016, Meeting Abstracts of the Physical Society of Japan, 71, 2850 - 2850, Japanese

  Summary national conference


• 21pAR-2 Relation Between Vertex-type Tensor Network States and IRF-type ones

  Nishino Tomotoshi

  The Physical Society of Japan, 2015, Meeting Abstracts of the Physical Society of Japan, 70, 2913 - 2913, Japanese


• 微分積分(第12回)お日さまは,まっすぐに昇るの?

  西野 友年

  日本評論社, Mar. 2011, 数学セミナー, 50(3) (3), 70 - 75, Japanese


• 25aTF-8 Hyperbolic Deformation Applied to Quantum Spin Chains : Scaling Relation in Excitation Energy

  Ueda H, Nakano H, Kusakabe K, Nishino T

  社団法人日本物理学会, Mar. 2011, Meeting abstracts of the Physical Society of Japan, 66(1) (1), 285 - 285, Japanese

  Summary national conference


• 微分積分(第11回)複素関数の心は虚々実々

  西野 友年

  日本評論社, Feb. 2011, 数学セミナー, 50(2) (2), 62 - 67, Japanese


• 微分積分(第10回)大波小波でフーリエ級数

  西野 友年

  日本評論社, Jan. 2011, 数学セミナー, 50(1) (1), 67 - 73, Japanese


• 25pTE-1 Phase Transition of the TFI Model under Hyperbolic Deformation

  Nishino Tomotoshi, Gendiar Andrej

  The Physical Society of Japan, 2011, Meeting Abstracts of the Physical Society of Japan, 66(1) (1), 293 - 293, Japanese


• 微分積分(第9回)微分方程式も好きずき

  西野 友年

  日本評論社, Dec. 2010, 数学セミナー, 49(12) (12), 68 - 73, Japanese


• 微分積分(第8回)我臼山(がうすやま)ブラブラ歩いて偏微分

  西野 友年

  日本評論社, Nov. 2010, 数学セミナー, 49(11) (11), 72 - 77, Japanese


• 微分積分(第7回)金の球を立方体から削り出す

  西野 友年

  日本評論社, Oct. 2010, 数学セミナー, 49(10) (10), 74 - 79, Japanese


• 微分積分(第6回)微分からね,積分を眺めたの

  西野 友年

  日本評論社, Sep. 2010, 数学セミナー, 49(9) (9), 62 - 67, Japanese


• 微分積分(第5回)麺を並べれば面になる積分の話

  西野 友年

  日本評論社, Aug. 2010, 数学セミナー, 49(8) (8), 70 - 75, Japanese


• Transverse Field Ising Model Under Hyperbolic Deformation

  Hiroshi Ueda, Andrej Gendiar, Valentin Zauner, Takatsugu Iharagi, Tomotoshi Nishino

  Ground state of the one-dimensional transverse field Ising model is
  investigated under the hyperbolic deformation, where the energy scale of j-th
  bond is proportional to the function \cosh ( j \lambda ) that contains a
  parameter \lambda. Although the Hamiltonian is position dependent, the ground
  state is nearly uniform and finitely correlated. We observe the energy cross
  over between the ordered and disordered state with respect to the transverse
  field. The model shows first order phase transition, and the discontinuities in
  the magnetization and entanglement entropy at the transition point...

  Aug. 2010

  Technical report


• 微分積分(第4回)明日へ向かってテイラー展開!

  西野 友年

  日本評論社, Jul. 2010, 数学セミナー, 49(7) (7), 66 - 71, Japanese


• 微分積分(第3回)微分計算の決まり手あれこれ

  西野 友年

  日本評論社, Jun. 2010, 数学セミナー, 49(6) (6), 58 - 63, Japanese


• 微分積分(第2回)指数関数と三角関数を微分しよう

  西野 友年

  日本評論社, May 2010, 数学セミナー, 49(5) (5), 68 - 73, Japanese


• 微分積分(第1回)まずは微分の心をつかめ

  西野 友年

  日本評論社, Apr. 2010, 数学セミナー, 49(4) (4), 72 - 76, Japanese


• 21pEA-5 Scale free property of Wilson numerical renormalization group

  Okunishi K., Nishino T.

  The Physical Society of Japan (JPS), 01 Mar. 2010, Meeting abstracts of the Physical Society of Japan, 65(1) (1), 300 - 300, Japanese


• 22pEH-15 Gap Estimation of One-Dimensional Quantum Spin Chains : Scaling Analysis with Hyperbolic Deformation

  Ueda H, Nakano H, Kusakabe K, Nishino T

  社団法人日本物理学会, Mar. 2010, Meeting abstracts of the Physical Society of Japan, 65(1) (1), 336 - 336, Japanese

  Summary national conference


• 23pTE-5 Scale free property of Wilson numerical renormalization group II

  Okunishi K., Nishino T.

  The Physical Society of Japan, 2010, Meeting Abstracts of the Physical Society of Japan, 65(2) (2), 218 - 218, Japanese


• 26pQK-10 Gap Estimation of One-Dimensional Quantum Spin Chains Using Hyperbolic Deformation

  Ueda H, Nakano H, Kusakabe K, Nishino T

  社団法人日本物理学会, Aug. 2009, Meeting abstracts of the Physical Society of Japan, 64(2) (2), 195 - 195, English

  Summary national conference


• 26pQK-9 Open Boundary Condition without Boundary

  Nishino Tomotoshi

  The Physical Society of Japan, 2009, Meeting Abstracts of the Physical Society of Japan, 64(2) (2), 195 - 195, Japanese


• 25pQD-8 Tensor Network Formulations Developed from DMRG

  Nishino T.

  The Physical Society of Japan, 2009, Meeting Abstracts of the Physical Society of Japan, 64(2) (2), 170 - 170, Japanese


• 23aWD-3 Phase transition of classical spin models on a hyperbolic lattice

  Ueda K., Nishino T., Gendiar A., Krcmar R.

  The Physical Society of Japan, 2008, Meeting Abstracts of the Physical Society of Japan, 63(1) (1), 263 - 263, Japanese


• 23aWD-2 Corner Transfer Matrix Renormalization Group on Hyperbolic Lattices

  Nishino T., Ueda K., Krcmar R., Gendiar A.

  The Physical Society of Japan, 2008, Meeting Abstracts of the Physical Society of Japan, 63(1) (1), 262 - 262, Japanese


• 22pTS-1 Numerical RG method for finite size area.

  Ueda Kouji, Nishino Tomotoshi

  The Physical Society of Japan, 2007, Meeting Abstracts of the Physical Society of Japan, 62(2) (2), 292 - 292, Japanese


• 18aWA-9 Real-time DMRG seen from principle of least action

  Ueda Kouji, Nishino Tomotoshi

  The Physical Society of Japan, 2007, Meeting Abstracts of the Physical Society of Japan, 62(1) (1), 237 - 237, Japanese


• 19pWA-13 DMRG like algorithm applied for a finite size cluster

  Nishino Tomotoshi

  The Physical Society of Japan, 2007, Meeting Abstracts of the Physical Society of Japan, 62(1) (1), 266 - 266, Japanese


• 26pYC-3 Scaling for finite size classical lattice system by matrix product states

  Ueda Kouji, Nishio Yukinobu, Nishino Tomotoshi

  The Physical Society of Japan, 2005, Meeting Abstracts of the Physical Society of Japan, 60(1) (1), 304 - 304, Japanese


• 27aYC-4 a particle in a box

  Jin chenglong, Ueda Kouji, Nishio Yukinobu, Nishino Tomotoshi

  The Physical Society of Japan, 2005, Meeting Abstracts of the Physical Society of Japan, 60(1) (1), 313 - 313, Japanese


• 21pXE-1 Iterative stacking expansion

  Ueda Kouji, Nishino Tomotoshi

  The Physical Society of Japan, 2005, Meeting Abstracts of the Physical Society of Japan, 60(2) (2), 185 - 185, Japanese


• 21pXE-2 Matrix Product Preparation in the Infinite System DMRG Algorithm

  Nishino T., Ueda K., Gendiar Andrej

  The Physical Society of Japan, 2005, Meeting Abstracts of the Physical Society of Japan, 60(2) (2), 185 - 185, Japanese


• 14aTB-3 Giound state study of quantum spin systems by Tensor product wave function

  Nishio Yukinobu, Ueda Kouji, Nishino Tomotoshi

  The Physical Society of Japan, 2004, Meeting Abstracts of the Physical Society of Japan, 59(2) (2), 228 - 228, Japanese


• 14pTB-12 Snapshot generation for classical spin system by CTMRG algorithm

  Ueda Kouji, Nishio Yukinobu, Nishino Tomotoshi

  The Physical Society of Japan, 2004, Meeting Abstracts of the Physical Society of Japan, 59(2) (2), 265 - 265, Japanese


• How to construct an appropriate RG transformation in DMRG

  Nishino Tomotoshi

  The Physical Society of Japan, 2003, Meeting Abstracts of the Physical Society of Japan, 58(2) (2), 244 - 244, Japanese


• Kramers-Wannier Approximation for 2D quantum Systems

  Vertex Weight, Nishino Tomotoshi

  The Physical Society of Japan, 2002, Meeting Abstracts of the Physical Society of Japan, 57(2) (2), 267 - 267, Japanese


• Matrix product state approximation for the maximum-eigenvalue eigenstate of the quantum transfer matrix

  Maeshima N., Akutsu Y., Nishino T., Okunishi K., Hieida Y.

  The Physical Society of Japan (JPS), 03 Sep. 2001, Meeting abstracts of the Physical Society of Japan, 56(2) (2), 186 - 186, Japanese


• Tensor Product Variational Formulation for 3D Potts Model : Stable Numerical Algorithm form > 2

  Nishino Tomotoshi

  The Physical Society of Japan, 2001, Meeting Abstracts of the Physical Society of Japan, 56(2) (2), 170 - 170, Japanese


• "Bochi-Bochi formula for 3D Classical Systems"

  Nishino Tomotoshi, Okunishi Kouichi

  The Physical Society of Japan, 2000, Meeting Abstracts of the Physical Society of Japan, 55(1) (1), 193 - 193, Japanese


• 3次元Isingモデルの密度行列繰り込み群 :-数値計算的側面について-

  西野 友年, 奥西 巧一

  報告

  大阪大学, Feb. 1999, 大阪大学大型計算機センターニュース, 111(28) (28), 39 - 49, Japanese


• 27aV-7 Kramers-Wannier Approximation for 3D Ising Model

  OKUNISHI K, NISHINO T, AKUTSU Y

  The Physical Society of Japan, 1999, Meeting Abstracts of the Physical Society of Japan, 54(2) (2), 282 - 282, Japanese


• 28p-XE-6 Optimization in DMRG:

  Nishino Tomotoshi, Takasaki Hiroshi

  The Physical Society of Japan, 1999, Meeting Abstracts of the Physical Society of Japan, 54(1) (1), 650 - 650, Japanese


• A way of understanding DMRG in 30 minutes

  NISHINO Tomotoshi

  The Physical Society of Japan, 1998, Meeting Abstracts of the Physical Society of Japan, 53(1) (1), 660 - 660, Japanese


• 8a-PS-91 Ground State of a Quantum Spin Chain in which Two S = 1/2 and Two S = 1 Spins are Arrenged Alternatively II

  Hikihara T., Tonegawa T., Nishino T., kaburagi M., Miyashita S.

  The Physical Society of Japan (JPS), 16 Sep. 1997, Meeting abstracts of the Physical Society of Japan, 52(2) (2), 828 - 828, Japanese


• 29a-YH-12 Ground State of a Quantum Spin Chain which Two S=1/2 and Two S=1 Spins are Arranged Alternatively

  Hikibara T, Tonegawa T, Nishino T, Kaburagi M, Miyashita S

  The Physical Society of Japan (JPS), 17 Mar. 1997, Meeting abstracts of the Physical Society of Japan, 52(1) (1), 705 - 705, Japanese


• 29p-YH-11 Themodynamics of a Quantum Spin Chain in which Two S=1/2 and Two S=1 Spins are Arranged Alternatively

  Tonegawa T, Hikibara T, Nishino T, Kaburagi M, Miyashita S

  The Physical Society of Japan (JPS), 17 Mar. 1997, Meeting abstracts of the Physical Society of Japan, 52(1) (1), 705 - 705, Japanese


• 密度行列繰り込み群の方法

  西野 友年, 柴田 尚和

  アグネ技術センタ-, Jan. 1997, 固体物理, 32(1) (1), 12 - 20, Japanese


• 7a-YJ-10 Corner Tensor Renormalization Group Method

  Tomotoshi Nishino

  The Physical Society of Japan, 1997, Meeting Abstracts of the Physical Society of Japan, 52(2) (2), 776 - 776, Japanese


• 29p-YH-6 Numerical Acceleration of DMRG by use of (q-) Group Symmetry

  Nishino Tomotoshi, Sierra German

  The Physical Society of Japan, 1997, Meeting Abstracts of the Physical Society of Japan, 52(1) (1), 704 - 704, Japanese


• Friedel oscillations in the one-dimensional Kondo lattice model

  Shibata Naokazu, Ueda Kazuo, Nishino Tomotoshi, Ishii Chikara

  The Physical Society of Japan (JPS), 13 Sep. 1996, Abstracts of the meeting of the Physical Society of Japan. Sectional meeting, 1996(3) (3), 228 - 228, Japanese


• 31a-YF-3 Spin and charge gaps in the 1D Kondo lattice model with Coulomb interactions

  Shibata Naokazu, Nishino Tomotoshi, Ueda Kazuo, Ishii Chikara

  The Physical Society of Japan (JPS), 15 Mar. 1996, Abstracts of the meeting of the Physical Society of Japan. Annual meeting, 51(3) (3), 21 - 21, Japanese


• 1a-YF-8 Corner Transfer Matrix Renormalization Group at Criticality

  Nishino Tomotoshi

  The Physical Society of Japan, 1996, Meeting Abstracts of the Physical Society of Japan, 51(3) (3), 80 - 80, Japanese


• Observation of the weak first order transition by CTMRG

  西野 友年, 奥西 巧一, 菊池 誠

  The Physical Society of Japan, 1996, Meeting Abstracts of the Physical Society of Japan, 1996(3) (3), 609 - 609, Japanese


• 31a-L-13 Product Wave Function Renormalization Group Method

  Okunishi K., Nishino T., Akutsu Y.

  The Physical Society of Japan, 1996, Meeting Abstracts of the Physical Society of Japan, 51(3) (3), 555 - 555, Japanese


• Spin-Fluid to Dimer Transition in the S=1/2 Heisenberg Chain with Strongly Competing Interactions II

  Shibata Y., Nishino T., Kaburagi M., Tonegawa T.

  The Physical Society of Japan (JPS), 12 Sep. 1995, Abstracts of the meeting of the Physical Society of Japan. Sectional meeting, 1995(3) (3), 612 - 612, Japanese


• ---古典2次元模型の分配関数の計算---

  西野 友年

  記事

  大阪大学, Sep. 1995, 大阪大学大型計算機センターニュース, 97(25) (25), 11 - 12, Japanese


• Fractional Quantum Hall States and Magic Numbers of Angular Momentum in Quantum Dot Systems

  Seki T, Nishino T, Kuramoto Y

  The Physical Society of Japan (JPS), 16 Mar. 1995, Abstracts of the meeting of the Physical Society of Japan. Annual meeting, 50(2) (2), 140 - 140, Japanese


• Density Matrix Renormalization Group for 2D Classical Systems

  Nishino Tomotoshi

  The Physical Society of Japan, 1995, Meeting Abstracts of the Physical Society of Japan, 1995(3) (3), 694 - 694, Japanese


• 29p-YG-8 Dynamic Correlation Functions of the 1-dimensional Kondo Lattice Model

  Nishino Tomotoshi, Ueda Kazuo

  The Physical Society of Japan, 1995, Meeting Abstracts of the Physical Society of Japan, 50(3) (3), 80 - 80, English


• ベクトル計算機用小規模行列の加算・乗算高速化支援プリプロセッサ : 短い DO ループを早く計算させたい方の為に

  西野 友年

  研究開発

  大阪大学大型計算機センター, Feb. 1994, 大阪大学大型計算機センターニュース, 91(91) (91), 3 - 12, Japanese


• 12a-S-3 Large Fermi Surface of the One-Dimensional Kondo-Lattice Model

  Ueda Kazuo, Nishino Tomotoshi, Tsunetsugu Hirokazu

  The Physical Society of Japan (JPS), 20 Sep. 1993, Abstracts of the meeting of the Physical Society of Japan. Sectional meeting, 1993(3) (3), 21 - 21, English


• 12p-S-3 Correlation Functions of One-Dimensional t-t' Kondo Lattice Model

  Nishino T., Ueda Kazuo

  The Physical Society of Japan, 1993, Meeting Abstracts of the Physical Society of Japan, 1993(3) (3), 29 - 29, Japanese


• 30a-S-12 Spin and Charge Excitation Gaps in One-Dimensional Periodic Anderson Model

  Nishino T., Ueda K.

  The Physical Society of Japan, 1993, Meeting Abstracts of the Physical Society of Japan, 48(3) (3), 51 - 51, Japanese


• 27p-PS-2 A new algorithm for Numerical Diaganalization of Quantum Spin System

  Kaburagi M, Tonegawa T, Nishino T

  The Physical Society of Japan (JPS), 12 Mar. 1992, 年会講演予稿集, 47(3) (3), 389 - 389, Japanese


• 28a-ZK-1 Two Dimensional Filtering method for the Hubbard Gap

  Nishino Tomotoshi

  The Physical Society of Japan, 1992, Meeting Abstracts of the Physical Society of Japan, 47(3) (3), 44 - 44, Japanese


• 28a-W-11 A Relationship between the S=1 Heisenberg Chain and an extended Hubbard Chain

  Nishino Tomotoshi

  The Physical Society of Japan, 1991, Meeting Abstracts of the Physical Society of Japan, 46(3) (3), 450 - 450, Japanese


• 3a-TD-7 Internal magnetic field at the La site in the La_2MO_4(M=Cu,Ni)

  Takahashi M., Nishino T.

  The Physical Society of Japan (JPS), 02 Oct. 1990, 秋の分科会講演予稿集, 1990(3) (3), 158 - 158, Japanese


• XPS Spectra of the d-p Model : Hole Distribution in Final State

  Nishino Tomotoshi

  The Physical Society of Japan, 1990, Meeting Abstracts of the Physical Society of Japan, 1990(3) (3), 298 - 298, Japanese


• 6a-ZA-1 X-ray spectroscopy of a system with translational invariance

  Nishino T., Kanamori J.

  The Physical Society of Japan, 1989, Meeting Abstracts of the Physical Society of Japan, 1989(3) (3), 364 - 364, Japanese


• 31a-PS-66 The Electronic Structure in Cu-O Pylamidal Plane

  Nishino T., Kikuchi M., Kanamori J.

  The Physical Society of Japan, 1989, Meeting Abstracts of the Physical Society of Japan, 44(3) (3), 239 - 239, Japanese


• 6p-PS-1 酸化物超伝導体の1モデル : P_zバンドとスピン系の相互作用

  西野 友年, 菊池 誠, 金森 順次郎

  一般社団法人 日本物理学会, 1988, 秋の分科会予稿集, 1988(3) (3), 327 - 327, Japanese

• テンソルネットワーク入門

  西野, 友年

  Single work, 単著, 講談社, Apr. 2023, Japanese, ISBN: 9784065316535


• テンソルネットワークの基礎と応用

  西野, 友年

  Single work, サイエンス社, Jun. 2021, Japanese, ISBN: 9784781915159

  Scholarly book


• "お理工さん"の微分積分

  西野, 友年

  Single work, 日本評論社, Sep. 2016, Japanese, ISBN: 9784535786813


• 今度こそわかる量子コンピューター

  西野, 友年

  Single work, 講談社, Oct. 2015, Japanese, ISBN: 9784061566057


• 今度こそわかる場の理論

  西野, 友年

  Single work, 講談社, Mar. 2012, Japanese, ISBN: 9784061532823


• ゼロから学ぶ解析力学

  西野, 友年

  Single work, 講談社, Jul. 2009, Japanese, ISBN: 9784061546844


• ゼロから学ぶベクトル解析

  西野, 友年

  Single work, 講談社, Mar. 2009, Japanese, ISBN: 9784061546622


• ゼロから学ぶエントロピー

  西野, 友年

  Single work, 講談社, Jul. 2007, Japanese, ISBN: 4061546694


• ゼロから学ぶ電磁気学

  西野, 友年

  Single work, 講談社, Apr. 2007, Japanese, ISBN: 9784061546721

• Tensor Network

  Tomotoshi Nishino

  Intensive Lecture (Tsukuba University), Nov. 2021, English

  Invited oral presentation


• Effects of energy scale deformations on discrete lattice Hamiltonians

  Tomotoshi Nishino

  Statphys seminar No. 15 (Online Seminar, Tokyo University), Nov. 2021, English

  Invited oral presentation


• Tensor Network Formulation

  Tomotoshi Nishino

  SQP Autumn School 2021, Sep. 2021, English

  [Invited]

  Invited oral presentation


• Ground State of the Heisenberg model on Polygon Lattices under the presence of large perturbation

  Tomotoshi Nishino

  日本物理学会2021年秋季大会, Sep. 2021, Japanese

  Oral presentation


• Sine Square Deformation: accidental finding from the entanglement

  Tomotoshi Nishino

  International Workshop on Tensor Networks in Many Body and Lattice Field (Shanghai), Jul. 2021, English

  [Invited]

  Invited oral presentation


• Suppression of boundary effect by the energy scale deformation in Fermionic systems

  Tomotoshi Nishino

  Physical Society of Japan, Mar. 2021

  Oral presentation


• Tensor Network for Statistical Mechanics

  Tomotoshi Nishino

  Entanglement in Strongly Correlated Systems (Benasque), Feb. 2021, English

  [Invited]

  Invited oral presentation


• Corner Transfer Matrix Formalism

  Tomotoshi Nishino

  European Tensor Network online seminar series, Dec. 2020

  [Invited]

  Invited oral presentation


• A century of the tensor network formulation

  Tomotoshi Nishino

  Quantum Tensor Networks and Machine Learning (NeuroIPS 2020 QTNML), Dec. 2020, English

  [Invited]

  Invited oral presentation


• Phase Transition of two-dimensional Octahedron model

  Tomotoshi Nishino, Andrej Gendiar, Roman Krcmar

  Physical Society of Japane, Sep. 2020, Japanese

  Oral presentation


• Adaptive Tree Tensor Network Expression for Quantum States I

  Tomotoshi Nishino, Yutaka Hashimoto, Hiroshi Ueda, Koichi Okunishi

  Physical Society of Japan, Mar. 2020

  Oral presentation


• Ising Model on a Fractal Lattice; where is the surface?

  Tomotoshi Nishino, Jozef Genzor, Andrej Gendiar

  Physical Society of Japan, Sep. 2019, Japanese

  Oral presentation


• 謝爾賓斯基(Sierpinski)三角形上の横磁場イジングをHOTRGで調べてみ

  Jozef Genzor, NISHINO Tomotoshi, Roman Krcmar, Andrej Gendiar

  日本物理学会第74回年次大会, Mar. 2019, Japanese, 日本物理学会, 九州大学, Domestic conference

  Oral presentation


• Technical details of quantum HOTRG calculation

  Jozef Genzor, NISHINO Tomotoshi, Roman Krcmar, Andrej Gendiar

  TNSAA2018-2019, Dec. 2018, English, RIKEN AICS, KOBE, International conference

  Poster presentation


• About HOTRG applied to the Sierpinski Carpet

  Jozef Genzor, NISHINO Tomotoshi, Roman Krcmar, Andrej Gendiar

  TNSAA2018-2019, Dec. 2018, English, RIKEN AICS, KOBE, International conference

  Poster presentation


• テンソルネットワーク

  Jozef Genzor, NISHINO Tomotoshi, Roman Krcmar, Andrej Gendiar

  研究会・離散手法による場と時空のダイナミクス, Sep. 2018, Japanese, 東北大学, Domestic conference

  [Invited]

  Invited oral presentation


• シェルピンスキーのホットカーペットにイジング乗せてみた

  Jozef Genzor, NISHINO Tomotoshi, Roman Krcmar, Andrej Gendiar

  日本物理学会2018年秋季大会, Sep. 2018, Japanese, 日本物理学会, 同志社大学, Domestic conference

  Oral presentation


• Optimization of Tensor Network Representation for Probability Distribution from the view point of Entanglem TNSAA2018ent”

  NISHINO Tomotoshi

  NTU-Kobe U joint workshop on Data Science and AI, Mar. 2018, English, 南洋理工大学, Singapore, International conference

  Public symposium


• Tensor Network Methods applied to lattices with recursive structure

  NISHINO Tomotoshi

  TNSAA2018, Jan. 2018, English, 中国科学院, Beijing, International conference

  [Invited]

  Nominated symposium


• 密度行列くりこみ群

  NISHINO Tomotoshi

  量子化学スクール, Dec. 2017, Japanese, 分子科学研究所, 岡崎, Domestic conference

  Public discourse


• Entanglement Structure in Random Spin Systems

  NISHINO Tomotoshi

  Workshop on Tensor-Network Methods, Dec. 2017, English, Simons Center, ＮＹ, International conference

  [Invited]

  Nominated symposium


• テンソルネットワーク形式の発展

  NISHINO Tomotoshi

  コロキウム, May 2017, Japanese, 日本大学, 東京, Domestic conference

  Public discourse


• シンポジウム公演 “行列積状態からテンソルネットワークへ: 形式と発展

  西野友年

  日本物理学会第72回 年次大会, Mar. 2017, Japanese, 大阪大学, 大阪大学, Domestic conference

  [Invited]

  Nominated symposium


• TEBD を用いた+-Jランダムイジングモデルのエンタングルメントエントロピーの解析

  笹川佳則, 西野友

  日本物理学会第72回年次大会, Mar. 2017, Japanese, 大阪大学, 大阪大学, Domestic conference

  Oral presentation


• Entanglement Entropy in Statistical Lattice Models

  西野友年

  Workshop on Quantum Dynamics and Response, Mar. 2017, English, 東京大学, 東京大学, Domestic conference

  Public discourse


• Analysis of Entanglement Entropy of the +-J Ising model using TEBD

  笹川佳則, 西野友

  Workshop on Numerical Methods andSimulations for Materials Design and Strongly Correlated Quantum Matters, Mar. 2017, English, 理化学研究所, 神戸大学, Domestic conference

  Nominated symposium


• Entanglement Entropy of q=6 Clock model

  西野友年

  TNSAA2016, Dec. 2016, English, NCTS 新竹, 台湾, International conference

  Oral presentation


• 正弦２乗変形: 非一様ハミルトニアンの下での一様性

  西野友年

  セミナー, Nov. 2016, Japanese, 広島大学, 広島大学, Domestic conference

  Public discourse


• 正方格子イジングモデルに空いた穴の周りのエンタングルメント

  西野友年

  日本物理学会2016年秋季大 会, Sep. 2016, Japanese, 金沢大学, 金沢大学, Domestic conference

  Oral presentation


• +-Jランダムイジングモデルのエンタングルメント・エントロピー

  西野友年, 上田宏

  ポスト京コンピュータ ー萌芽的課題1サブ課題D「量子力学と情報」研究会, Sep. 2016, Japanese, ISSP, 東京大学, Domestic conference

  Oral presentation


• テンソルネットワーク形式と、その応用

  西野友年

  物性若手夏の学校, Jul. 2016, Japanese, 物性若手夏の学校準備局, ホテルシャレードイン 滋賀, Domestic conference

  Public discourse


• Tensor Product States applied to Statistical Lattice Models

  T. Nishino

  Tensor Networks and Quantum Many-Body Problems, Jul. 2016, English, ISSP, 東京大学, Domestic conference

  Oral presentation


• Mean-field Behavior in Uniform Tensor Product State

  T. Nishino

  Tensor Networks and Quantum Many-Body Problems, Jul. 2016, English, ISSP, 東京大学, Domestic conference

  Oral presentation


• Higher Order Tensor Renormalization Group (HOTRG) によるフラクタル Ising 模型の相転移解析

  西野友年

  日本物理学会第71回年次大会, Mar. 2016, Japanese, 東北学院大学, Domestic conference

  Oral presentation


• 6状態クロック模型のBKT転移をエンタングルメントから眺 めてみれば、あまのかぐやま

  西野友年, Roman Krcmar, Andrej Gendiar

  日本物理学会第72回年次大会, Mar. 2016, Japanese, 大阪大学, 大阪大学, Domestic conference

  Oral presentation


• Phase transition of Classical Ising Model on 2D Fractal Lattice

  T. Nishino

  TNSAA2016, Jan. 2016, English, 分子化学研究所, Domestic conference

  Oral presentation


• Renormalization Group Transformation applied to Interaction-Round-a-Face (IRF) Model

  T. Nishino

  workshop and Symposium on DMRG Technique for Strongly Correlated Systems in Physics and Chemistry, Jun. 2015, English, Natal, International conference

  [Invited]

  Invited oral presentation


• One Particle Basis under non-uniform Deformation

  T. Nishino

  Novel Computational Methods for Quantitative Electrnic Structure Calculations, Jun. 2015, English, 神戸大学, Domestic conference

  [Invited]

  Invited oral presentation


• 私は Vertex、あなたは IRF、テンソルネットワークも好き好き

  NISHINO TOMOTOSHI

  日本物理学会第70回年次大会, Mar. 2015, Japanese, 早稲田大学, Domestic conference

  Poster presentation


• Corner Line Structure of the Density Matrix Spectrum in Real-Space Renormalization Group

  T. Nishino

  Workshop on New Frontier of Numerical Methods for Many-Body Correlations, Feb. 2015, English, 東京大学, International conference

  Public symposium


• Placket type local weight and tensor product state

  T. Nishino

  workshop on Tensor Network States: Algorithm and Applications, Dec. 2014, English, 中国科学院, International conference

  Public symposium


• a Blackboard Talk on Sine Square Deformation

  T. Nishino

  workshop on Numerical and Analytical Methods for Strongly Correlated Systems, Sep. 2014, English, Benasque, International conference

  Public symposium


• The most distant sites are neighbors under the sine square deformation

  T. Nishino

  Workshop on Numerical Many Body Methods in Quantum Chemistry and Physics, Dec. 2013, English, Bangalore, International conference

  [Invited]

  Invited oral presentation


• Entanglement Spectrum in the Tensor Renormalization Group

  T. Nishino

  PQMBE2013, Sep. 2013, English, Maintz, International conference

  Poster presentation


• What should be Approximated in RG schmes applied to Statistical Models?

  T. Nishino

  Tensor Network Algorithms in Computational Physics and Numerical Analysis, May 2013, English, ETH Zurich, International conference

  [Invited]

  Invited oral presentation


• DMRG applied to Transfer Matrix Formalisms

  NISHINO Tomotoshi

  DMRG101, Dec. 2012, English, Taiwan University, Taipei, Taiwan, 密度行列繰り込み群の背景について解説した, International conference

  [Invited]

  Invited oral presentation


• Entanglement Entropy under non-Uniform Deformation

  NISHINO Tomotoshi

  QISM2012, Sep. 2012, English, UAM, Innsbruck University, Innsbruck, Austria, 非一様なエネルギースケール変形がかかった１次元量子系のエンタングルメントエントロピーを求め、これを解説した, International conference

  Poster presentation


• Non-Uniform Deformation Applied to 1D Quantum Systems

  NISHINO Tomotoshi

  Networking Tensor Network, May 2012, English, CSIC, MPQ, Benasque, Spain, 非一様なエネルギースケール変形がかかった１次元量子系の基底状態を解析し、これを解説した, International conference

  [Invited]

  Invited oral presentation


• Hubbard Model に正弦変形かけてみちゃったの

  NISHINO TOMOTOSHI, Andrej Gendiar

  日本物理学会2012年 年会, Mar. 2012, Japanese, 関西学院大学, Domestic conference

  Oral presentation


• Sine-Square Deformation

  T. Nishino

  Seminar at ITP (中国科学院), Feb. 2012, English, Beijing, China, International conference

  Oral presentation


• エンタングルメントで解決できるもの、できないもの

  NISHINO TOMOTOSHI

  基研研究会「量子系のエンタングルメントとくりこみ群」, Dec. 2011, Japanese, 基礎物理学研究所, Domestic conference

  Oral presentation


• Ising Model on Hyperbolic Lattices

  T. Nishino

  UCM Summer School, Jul. 2011, English, El Escorial, International conference

  Oral presentation


• Absence of Boundary Effect under Sine-Square Deformation

  T. Nishino

  QISM2011, Jul. 2011, English, A Coruna, International conference

  Oral presentation


• Hyperbolic and Sinusoidal Deformations

  T. Nishino

  International Workshop on Tensor Networks, Feb. 2011, English, Brisbane, Australia, International conference

  Oral presentation


• Wave Function Prediction; a Classical Background

  T. Nishino

  from DMRG to Tensor Network Formulations, Oct. 2010, English, Domestic conference

  Oral presentation


• An Origin of Matrix Productt States in Statistical Mechanics

  T. Nishino

  Workshop on DMRG and other advances in numerical RG methods (August 2010, Beijing), Aug. 2010, English, Beijing, China, International conference

  Oral presentation


• Phase Transition on Hyperbolic Lattice Analyzed by CTMRG

  T. Iharagi, H. Ueda, T. Nishino

  STATPHYS24, Jul. 2010, English, Cairns, Australia, International conference

  Oral presentation


• Tensor Network State in Statistical Physics

  T. Nishino, A. Gendiar

  Workshop on Theoretical Aspects of Tensor Network States, Oct. 2009, English, Universidad Complutense de Madrid, International conference

  Oral presentation


• Corner Transfer Matrix Renormalization Group applied to Ising Model on Hyperbolic Lattices

  T. Nishino, A. Gendiar

  発表会議名, Sep. 2009, English, RWTH Aachen University, International conference

  Oral presentation


• a DMRG Algorithm for finite size clusters

  Nishino Tomotoshi

  日本物理学会, Mar. 2007, Japanese, 鹿児島大学, Domestic conference

  Oral presentation


• Two dimensional Tensor Product State: Application to 3D Ising model and 2D Heisenberg model

  NISHINO Tomotoshi

  ワークショップ "Recent Progress and Prospects in Density Matrix Renormalization", Aug. 2004, English, 未記入, ライデン、オランダ, International conference

  Oral presentation


• 2次元量子スピン系基底状態のテンソル積変分による評価

  西野 友年

  日本物理学会, Sep. 2003, Japanese, 日本物理学会, 岡山大学, Domestic conference

  Oral presentation


• 2,3次元古典格子模型のブロックスピン変換、密度行列繰り込みの変分原理

  西野 友年

  京都大学数理解析研究所研究会「繰り込み群の数理科学での応用」, Sep. 2003, Japanese, 京都大学数理解析研究所, 京都大学, Domestic conference

  Oral presentation

• 物理教育学会


• Physical Society of Japan

• テンソルネットワーク形式を用いたエンタングルメント構造の数値的解析

  Tomotoshi Nishino

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2021 - Mar. 2025


• Entanglement Structure Analysis of Non-Uniform Systems by Tensor Network Formulation

  Tomotoshi Nishino

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2017 - Mar. 2021

  スケール変換に対しては一様系に似た振る舞いを持ち、かつ並進対称性がないフラクタル格子上の古典スピンおよび量子スピン系が非自明な相転移を起こす事実について、２次元的な結合を持つシェルピンスキー三角形や、同カーペット上の格子系でこれまで確認して来た。本年度は新たに、３次元的な結合を持つシェルピンスキーピラミッド格子上の量子イジング模型と、その拡張である３状態量子ポッツ模型について、横磁場に対する量子相転移の特異性を、高次特異値分解を用いたテンソルネットワーク形式により数値的に解析した。その結果、自発磁化が示す臨界指数は、２次元量子イジング模型が示す特異性から外れ、１次元量子イジング模型側に寄っていることが判明した。シェルピンスキーピラミッドのフラクタル次元は２であることから、格子のフラクタル次元が、その上に乗った模型の臨界現象に対して、直ちに反映されるものではないことが、以上の数値解析から新たに判明した。もう一つの研究の柱として、一様な２次元系が臨界状態にある状況を、半無限の非一様な量子１次元系と解釈することにより、対応する量子的な情報量であるエンタングルメント・エントロピーを数値計算により求め、相転移現象の解明を行うアプローチについても、前年度までに引き続き取り組んでいる。１格子点あたりの自由度が大きな古典スピン模型の例として、６状態クロック模型、１２及び２０自由度の正多面体模型、そして内部空間の次元が４以上である十字ポリトープ模型などの熱力学解析に着手している。その中で、６状態クロック模型については、エンタングルメント・エントロピーを用いればコスタリッツ・サウレス相の境界を精密に確定できることが確認できた。数値データの統計的な取り扱いにおいては、原田によるベイズ推定のアルゴリズムを用い、先見的な知識を用いずにスケーリング関数の形を確定した。


• Analysis of Phase Transitions from the view point of Entanglement

  Tomotoshi Nishino, Jozef Genzor

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows, Grant-in-Aid for JSPS Fellows, Kobe University, Jul. 2017 - Mar. 2019

  昨年度に引き続きフラクタル系について、テンソルネットワーク形式を用いたフラクタル系の数値解析を行い、得られた結果を報文に取りまとめる作業を行なった。代表的なフラクタルであるシェルピンスキー三角形の上に構築された横磁場イジング模型の基底状態解析を、高次テンソル繰り込み群手法(HOTRG)によって行なった所、横磁場の強さに応じて秩序・無秩序転移が起きることが確認できた。また、その際の臨界指数が、２次元以上３次元以下の古典イジング模型に相当する値となることが判明した。但し、この有効的な空間次元が、格子のフラクタル次元と一致しているようには見えなかった。これらの結果を論文に取りまとめ、出版した。特に計算上のテクニカルな問題として、初期テンソルの構成方法に注意が必要であることを、空間方向・虚時間方向のそれぞれについてのエンタングルメント・エントロピーの値から示し、効果的な対策について、提言を行なった。新たな取り組みとして、結合が密なフラクタルである、シェルピンスキー・カーペット上の古典イジングモデルの熱力学的性質についても、HOTRG 法を用いた数値解析を行なった。このフラクタルは、一見すると８個の四角い部分系から構成されているように見えるが、その見かけに従って系を分割することは、系か持つ自然なエンタングルメント構造を破壊することに等しい。なるべく少ない結合を切ることによって、系を分解することが重要である。この見地に基づき、斜め方向に系を切り分け、再起的にフラクタルを構成して行く形で、HOTRG 法に用いる局所テンソルを与えた。結果として、秩序・無秩序転移が起き、２次元以下の系に相当する臨界指数が観測された。また、局所的な物理量を観察すると、その振る舞いが格子状の場所によって大きく異なることが判明した。これらの結果を報文に取りまとめ、プレプリントとして公開した。


• Renormalization group analysis of energy-scale deformation by means of tensor-network formulations

  Nishino Tomotoshi

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2013 - Mar. 2017

  We investigated several types of lattice models under the energy scale deformation, where the local interaction strength is modulated slowly compared with the lattice constant, by means of numerical calculation assisted by the tensor network formulations. From the obtained thermal equilibrium states, behavior of entanglement entropy is analyzed with respect to temperature and parameters. In case of Ising model on hyperbolic lattices, which has a small negative curvature, its critical behavior is mean-field like, and the correlation length is bounded around the curvature radius even at the phase transition point. In the study of discrete Heisenberg model on two-dimensional lattice, various types of phase transitions are observed according to the manner of discretization. For example, we observed 1st order phase transition, and the Berezinskii-Kosterlitz-Thouless one, etc. We have also developed numerical methods for fractal systems and for tracing wave packets on 1D lattice.


• 古典および量子系の双曲変形

  Tomotoshi Nishino, KRCMAR Roman

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows, Grant-in-Aid for JSPS Fellows, Kobe University, Apr. 2012 - Mar. 2015

  前年度に引き続き、格子上の磁性模型について、角転送行列繰込み群（ＣＴＭＲＧ）を用いた数値解析を行った。本年度に着目したものは、６状態クロック模型である。この模型を双曲格子上に置くと、１次相転移を示す。一方、平面格子上ではコスタリッツ・サウレス（ＫＴ）転移を示し、有限幅の温度領域内で相関長が発散する臨界状態が実現することが知られている。ＫＴ転移において、角転送行列から得られる密度行列の固有値分布と、対応するエンタングルメント・エントロピー（ＥＥ）の「有限状態スケーリング」に対する振る舞いは、知られていない。臨界領域でＥＥが発散していることは、ほぼ自明であるが、ＣＴＭＲＧにおいて密度行列自由度χを制限した場合、ＥＥがどのような値を持つかは不明なのだ。そこで、全温度領域で秩序変数、内部エネルギー、ＥＥを計算し、パラメターχの選んだ値ごとに観察した。その結果、低温秩序相と臨界領域の間ではＥＥが温度に対して単調に増加するが、臨界相と高温無秩序相の間では小さなピークを持つことが判明した。このピークの位置と高さはχに依存していて、「有限χスケーリング」を行うことにより高温側の転移温度ＴＣ２を比較的精度良く求められることが判明した。また、臨界領域におけるＥＥの値そのものは、χに対して対数的に上昇して行くことが判明し、これを足がかりにしつつ低温側の転移温度ＴＣ１の推定も行った。このようにして得られた臨界領域の位置は、これまでにモンテカルロ計算により推定されていたものと一致した。これらの結果を踏まえ、これから先は双曲格子と平面格子を結ぶ、弱く負に曲がった格子上で、６状態クロック模型が示す臨界現象を追う研究を進めるとともに、これまでに得られた成果について論文として取りまとめて行く予定である。


• Optimization of tensor network states by means of a minimal principle and applications to quantum systems

  NISHINO Tomotoshi

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2010 - Mar. 2013

  The tensor network states has a hight potential of expressing or approximating a given quantum state wave function. For an efficient optimization of each local tensor, the construction of the environment around the tensor is important. In this study, we focus on the boundary condition, i.e. the smooth boundary condition, where the interaction parameter gradually decreases to zero toward the system boundary, the hyperbolic deformation, where the parameter increases to the boundary. These conditions are imposed to one dimensional free or correlated quantum systems. Under these deformation, despite of the non-uniformity in the Hamiltonian, the corresponding ground state is uniform, and the local tensors are optimized in a homogeneous manner. The fact is confirmed by means of the density matrix renormalization group, which is a representative numerical tool to optimize local tensors. Several other trials on the tensor network state are also reported.


• DMRG and Quantum Heat Bath - Principles and Applications -

  NISHINO Tomotoshi

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Kobe University, 2007 - 2008

  1次元量子系を2つの部分に分けて取り扱う場合、両者の量子相関はエンタングルメントと呼ばれる物理量によって記述でき、その定量評価は量子エントロピーによってなされる。1次元量子系の背後にある2次元古典系を、いわゆる古典・量子対応を通じて考察した結果、負の曲率を持った2次元古典系が対応する場合には量子エントロピーが抑えられることが判明した。また、正方形領域の分配関数と行列積変分関数の関係より、積波動関数を効率良く生成する計算アルゴリズムを開発した。


• DMRGの新展開－テンソル積分解と最適化の視点から－

  西野 友年

  科学研究費補助金／基盤研究(C), 2005, Principal investigator

  Competitive research funding


• Analysis of Higher Dimensional Systems by use of the Tensor Product Variational Approach

  NISHINO Tomotoshi

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), kobe University, 2001 - 2002

  We have developed a new numerical renormalization group (RG) method for two-dimensional (2D) quantum systems and 3D classical systems, using a variational state represented as a product of local weights. As an example, we employed 2D IRF model, that contains 3 parameters, as a variational state for the square lattice S=1/2 XXZ model, which is one of the representative 2D quantum systems. We obtained a good energy estimate, even though we have only 3 parameters. In this case the variational formulation works better in the anisotroplc limit, the XY mdoel. For the application for 3D Classical systems, we choose 3D lsing model as a reference system, and prepare a variational state that contains 162 variational parameters. In this case the local factor has auxiliary spin variable, that can be interpreted as the renormalized spin. Since there are so many parameters, one has to survey them automaticaliy. For this purpouse we developed a self-consistent equation for the local weight, and improve them vie iterative numerical procedure. As a result, we showed that the phase transition temperature is obtained accurately within the error of 1%. In the above cases, the variational state is uniform. This Is because CTMRG, the numerical RG method we have used, can treat uniform 2D models only. In order to improve this restriction, we considered a usage of the density matrix renormalization group (DMRG) for the system that have non-uniform ground state. As an example, we have started calculations of thermal state hi the ANNNI model, which has been considered to have complex structure in the ordered phase that appears in the Intermediate temperature. At present, we get a partial phase diagram, that suggests the suppression of the area of comensulate phase. As a bi-product of these researches, we unexpectedly get a new usage of CTMRG for the stochastic systems. The system has a kind of speed of light and information can be transferred within the light cone. We find a new targeting scheme for this case, and proposed a new numerical RG method, "the Ught Cone CTMRG method". Depending on the parameter condition the method becomes instable, and to improve this drawback is one of the task in the future studies


• Extension of DMRG by explicit construction of Density Matrices

  NISHINO Tomotoshi

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Kobe University, 1999 - 2000

  In the finite temperature density matrix renormalization group (DMRG) they normally construct the density matrices by cutting a cylinder which correspond ; to the finite temperature one-dimensional (ID) quantum systems. In this case, the topology of the 2D system (= cylinder) is different from the plane, conventional and simple construction of the density matrix is not always most efficient in the sense of free-energy minimum. This is because there is information exchange around the cylinder, which is not properly included by the conventional method. There is similar difficulty in DMRG for 3D classical systems. We thus return back to the principle of DMRG, we consider an efficient construction of the density matrix from the view point of the variational states represented as tensor product and their improvements. As a result, we obtained an equation that optimizes the tensor product state. In addition, we find that the equation can be solved numerically by way of the corner transfer renormalization group method (CTMRG). We apply the new variational method thus obtained, the tensor product variational approxi-mation (TPVA) to 3D Ising and Potts models, and obtained the transition temperatures and latent heats, that are comparable to those obtained by Monte Carlo simulations. We also drawed the phase diagram of the 16-vertex model by applying CTMRG method to the 16-vertex model, in the parameter region that is not investigated so far.


• 密度行列繰り込み群を基にした格子モデルの解析

  Tomotoshi Nishino

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Encouragement of Young Scientists (A), Grant-in-Aid for Encouragement of Young Scientists (A), Kobe University, 1996 - 1996

  臨界現象の基本概念の一つである繰り込み群をもとにしてWhiteが開発した密度行列繰り込み群と、Baxterにより2次元古典系の解析の為に導入された角転送行列の方法を組み合わせることによって、新たに「角転送行列繰り込み群」の方法を開発した。この方法を代表的な2次元古典系であるq状態Potts模型の臨界点での解析に応用した。一辺の長さがLの正方形クラスターに対して有限サイズスケーリングを行った結果、次の様な結果が得られた:(1)まずq=2,3Potts模型について、クラスター中心でのスピン相関と磁化のL依存性を測定し、角転送行列繰り込み群により精密な臨界指数の決定が可能である事を実証した。(2)q=4Potts模型については、見かけ上の臨界指数が理論的に予想されるものとずれる事実に代表されるLog補正の効果を精密測定し、補正項の係数を数値的に決定した。(3)従来、数値的に評価する事が困難であったq=5Potts模型の潜熱を、転移点でのサイト・エネルギーの飛びを直接評価することによって求められる事を示した。(4)q>5Potts模型の潜熱も、q=5の場合と同じく簡単に評価出来る事がわかった。以上の成果をふまえて、厳密解の知られていない、フラストレーションを持つ交差ボンド・イジング模型に対して臨界指数のスピン長S依存性を追跡した。その結果として、S=1/2の場合の臨界指数はS=1の場合のそれと等しいことが明らかになった。

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