New Development of the Density Matrix Renormalization Group Method based on Quantum Entanglement and Geometrical Phases

• Project/Area Number: 20740214
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Osaka University
• Principal Investigator: MARUYAMA Isao 大阪大学, 基礎工学研究科, 特任助教(常勤) (20422339)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 計算物理 / 物性物理 / 情報基礎 / 幾何学 / 密度行列繰り込み群 / 幾何学的位相 / 量子絡み合い / 密度行列繰りこみ群

Research Abstract

The matrix product state(MPS) is used as a variational state in the density matrix renormalization group(DMRG) method. We studied the MPS both numerically and analytically and published the papers that show the importance of the boundary matrix. In the exact solution, we obtained an extension of the MPS from the lattice toward the continuous space.

Research Products

• [Journal Article] Quantum Entanglement of Tensor Networks with Symmetry Projections (2012)
  • Author(s): M. Orii, H. Ueda, I. Maruyama
  • Journal Title: J. Phys. Soc. Jpn. Volume: 81
  • NAID: 210000109467
  • Peer Reviewed
• [Journal Article] Quantum Entanglement of Tensor Networks with Symmetry Projections (2012)
  • Author(s): Masashi Orii
  • Journal Title: Journal of the Physical Society of Japan Volume: 81 Issue: 4 Pages: 043001-043001
  • DOI: 10.1143/jpsj.81.043001
  • Peer Reviewed
• [Journal Article] Sine-square deformation of free fermion systems in one and higher dimensions (2011)
  • Author(s): I. Maruyama, H. Katsura, T. Hikihara
  • Journal Title: Phys. Rev. B Volume: 84
  • Peer Reviewed
• [Journal Article] ZQ Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices (2011)
  • Author(s): Y. Hatsugai, I. Maruyama
  • Journal Title: Euro Phys Letter Volume: 95
  • Peer Reviewed
• [Journal Article] Uniform Matrix Product State in the Thermodynamic Limit (2011)
  • Author(s): H. Ueda, I. Maruyama, K. Okunishi
  • Journal Title: J. Phys. Soc. Jpn. Volume: 80
  • NAID: 40018273836
  • Peer Reviewed
• [Journal Article] Sine-square deformation of free fermion systems in one and higher dimensions (2011)
  • Author(s): I.Maruyama, H.Katsura, T.Hikihara
  • Journal Title: Phys.Rev.B Volume: 84 Issue: 16
  • DOI: 10.1103/physrevb.84.165132
  • Peer Reviewed
• [Journal Article] Z_Q Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices (2011)
  • Author(s): Y.Hatsugai, I.Maruyama
  • Journal Title: Euro Phys Letter Volume: 95 Issue: 2 Pages: 20003-20003
  • DOI: 10.1209/0295-5075/95/20003
  • Peer Reviewed
• [Journal Article] Z_2 topological number of local quantum clusters in the orthogonal dimer model (2011)
  • Author(s): I.Maruyama, S.Tanaya, M.Arikawa, Y.Hatsugai
  • Journal Title: J.Phys.Conf.Ser. Volume: 32
  • Peer Reviewed
• [Journal Article] Uniform Matrix Product State in the Thermodynamic Limit (2011)
  • Author(s): H.Ueda, I.Maruyama, K.Okunishi
  • Journal Title: J.Phys.Soc.Jpn. 80
  • NAID: 40018273836
  • Peer Reviewed
• [Journal Article] Uniform Matrix Product State in the Thermodynamic Limit (2011)
  • Author(s): H.Ueda, I.Maruyama, K.Okunishi
  • Journal Title: J.Phys.Soc.Jpn. Volume: 80
  • NAID: 40018273836
  • Peer Reviewed
• [Journal Article] Ferromagnetism in the Hubbard model with topological/ non-topological flat bands (2010)
  • Author(s): Hosho Katsura, Isao Maruyama, Akinori Tanaka, Hal Tasaki
  • Journal Title: Europhys. Lett. Volume: 91
  • Peer Reviewed
• [Journal Article] Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction (2010)
  • Author(s): Isao Maruyama, Hosho Katsura
  • Journal Title: J. Phys. Soc. Jpn. Volume: 79
  • NAID: 40017205425
  • Peer Reviewed
• [Journal Article] Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands (2010)
  • Author(s): Hosho Katsura, Isao Maruyama, Akinori Tanaka, Hal Tasaki
  • Journal Title: Euro.Phys.Lett. 91
  • Peer Reviewed
• [Journal Article] Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction (2010)
  • Author(s): Isao Maruyama, Hosho Katsura
  • Journal Title: J.Phys.Soc.Jpn. 79
  • NAID: 40017205425
  • Peer Reviewed
• [Journal Article] Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz (2010)
  • Author(s): H.Katsura, I.Maruyama
  • Journal Title: J.Phys.A. : Math.Gen. 43
  • Peer Reviewed
• [Journal Article] Ferromagnetism in the Hubbard model with topological/non-topological flat bands. (2010)
  • Author(s): Hosho Katsura, Isao Maruyama, Akinori Tanaka, Hal Tasaki
  • Journal Title: Europhys.Lett. Volume: 91
  • Peer Reviewed
• [Journal Article] Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction (2010)
  • Author(s): Isao Maruyama, Hosho Katsura
  • Journal Title: J.Phys.Soc.Jpn. Volume: 79
  • NAID: 40017205425
  • Peer Reviewed
• [Journal Article] Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction (2010)
  • Author(s): Isao Maruyama, Hosho Katsura
  • Journal Title: J.Phys.A : Math.Gen. Volume: 43
  • NAID: 40017205425
  • Peer Reviewed
• [Journal Article] Topological identification of a spin-two-leg ladder with four-spin ring exchange (2009)
  • Author(s): I.Maruyama, T.Hirano, Y.Hatsugai
  • Journal Title: Phys.Rev.B. 79
  • Peer Reviewed
• [Journal Article] Quantized Berry Phases of a Spin-1/2 Frustrated Two-Leg Ladder with Four-Spin Exchange (2009)
  • Author(s): I.Maruyama, T.Hirano, Y.Hatsugai
  • Journal Title: J.Phys. : Conf.Ser. 145
  • Peer Reviewed
• [Journal Article] Topological Identification of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange (2009)
  • Author(s): I.Maruyama, T. Hirano, Y. Hatsugai
  • Journal Title: Phys. Rev. B 79
  • Peer Reviewed
• [Journal Article] Quantized Berry Phases of a Spin-1/2 Frustrated Two-Leg Ladder with Four-Spin Exchange (2009)
  • Author(s): I. Maruyama, T. Hirano, Y. Hatsugai
  • Journal Title: J. Phys. : Conf. Ser 145
  • Peer Reviewed
• [Journal Article] Quantum Entanglement of Tensor Networks with Symmetry Projections
  • Author(s): M.Orii, H.Ueda, I.Maruyama
  • Journal Title: J.Phys.Soc.J.Supplement Proc.TOKIMEKI2011 Volume: (印刷中)
  • NAID: 210000109467
  • Peer Reviewed
• [Journal Article] Application of Uniform Matrix Product State to Quantum Phase Transition with a Periodicity Change
  • Author(s): H.Ueda, I.Maruyama
  • Journal Title: J.Phys.Soc.J.Supplement Proc.TOKIMEKI2011 Volume: (印刷中)
  • Peer Reviewed
• [Presentation] 非整合周期をもつ一様行列積状態における最適化法の改良 (2012)
  • Author(s): 上田宏, 丸山勲
  • Organizer: 日本物理学会第67回年次大会領域11 26pAG-12
  • Place of Presentation: 関西学院大学(兵庫県)
  • Year and Date: 2012-03-26
• [Presentation] ZQ topological invariants for identification of short rangeentangled states (2012)
  • Author(s): I. Maruyama, S. Tanaya, Y. Hatsugai
  • Organizer: アメリカ物理学会
  • Place of Presentation: Boston(USA)
  • Year and Date: 2012-03-02
• [Presentation] Z_Q topological invariants for identification of short rangeentangled states (2012)
  • Author(s): I.Maruyama, S.Tanaya, Y.Hatsugai
  • Organizer: アメリカ物理学会
  • Place of Presentation: Boston(USA)
  • Year and Date: 2012-03-02
• [Presentation] Zigzag鎖における磁化プラトーの一様行列積状態による評価 (2012)
  • Author(s): 上田宏, 丸山勲
  • Organizer: フラストレーションが創る新しい物性最終成果報告会
  • Place of Presentation: 大阪大学銀杏会館(大阪府)
  • Year and Date: 2012-01-07
• [Presentation] 一様行列積状態における境界行列 (2011)
  • Author(s): 丸山勲
  • Organizer: 基研研究会「量子多体系のエンタングルメントとくりこみ群」
  • Place of Presentation: 京都大学基礎物理学研究所(京都府)
  • Year and Date: 2011-12-15
• [Presentation] 低次元量子スピン系に対する非整合周期行列積状態 (2011)
  • Author(s): 上田宏, 丸山勲
  • Organizer: 基研研究会「量子多体系のエンタングルメントとくりこみ群」
  • Place of Presentation: 京都大学基礎物理学研究所(京都府)
  • Year and Date: 2011-12-15
• [Presentation] 少数スピン系におけるテンソルネットワークと射影の効果 (2011)
  • Author(s): 折井仁嗣, 上田宏, 丸山勲
  • Organizer: 基研研究会「量子多体系のエンタングルメントとくりこみ群」
  • Place of Presentation: 京都大学基礎物理学研究所(京都府)
  • Year and Date: 2011-12-15
• [Presentation] Application of Uniform Matrix Product State to Quantum Phase Transition with a Commensurate/Incommensurate Change (2011)
  • Author(s): Hiroshi Ueda, Isao Maruyama
  • Organizer: International workshop on heavy fermions TOKIMEKI 2011
  • Place of Presentation: 大阪大学(大阪府)
  • Year and Date: 2011-11-25
• [Presentation] Demonstration of a New Numerical Calculation in Quantum Spin System (2011)
  • Author(s): Masashi Orii, Hiroshi Ueda, Isao Maruyama
  • Organizer: International workshop on heavy fermions TOKIMEKI 2011
  • Place of Presentation: 大阪大学(大阪府)
  • Year and Date: 2011-11-25
• [Presentation] Variational States Representing Large Entanglement Entropy for Small Spin Systems (2011)
  • Author(s): Masashi Orii, Hiroshi Ueda, Isao Maruyama
  • Organizer: 7th Handai Nanoscience and nanotechnology International Symposium-Nanoscience and nanotechnology in the Next Ten Years-
  • Place of Presentation: 大阪大学(大阪府)
  • Year and Date: 2011-11-11
• [Presentation] 一般スピンVBS状態におけるエンタングルメントとKennedy-Tasaki変換 (2011)
  • Author(s): 丸山勲
  • Organizer: 日本物理学会2011年秋季大会
  • Place of Presentation: 富山大学(富山県)
  • Year and Date: 2011-09-23
• [Presentation] 一般スピンVBS状態におけるエンタングルメントとKennedy-Tasaki変換 (2011)
  • Author(s): 丸山勲
  • Organizer: 日本物理学会2011年秋季大会,23aGU-5
  • Place of Presentation: 富山大学(富山県)
  • Year and Date: 2011-09-23
• [Presentation] 熱力学的極限での一様行列積状態と非整合周期 (2011)
  • Author(s): 上田宏, 丸山勲
  • Organizer: 日本物理学会2011年秋季大会,21pGA-7
  • Place of Presentation: 富山大学(富山県)
  • Year and Date: 2011-09-21
• [Presentation] 量子絡み合いとエネルギー精度:少数スピン系におけるテンソルネットワーク (2011)
  • Author(s): 折井仁嗣, 上田宏, 丸山勲
  • Organizer: 日本物理学会2011年秋季大会,21pGA-4
  • Place of Presentation: 富山大学(富山県)
  • Year and Date: 2011-09-21
• [Presentation] Z_Q topological invariants of gapped quantum systems for integer Q (2011)
  • Author(s): I.Maruyama, Y.Hatsugai
  • Organizer: 26^<th> International Conference on Low Temperature Physics(LT.26)
  • Place of Presentation: Beijin (China)
  • Year and Date: 2011-08-15
• [Presentation] Topological invariants based on Berry phases for frustrated systems (2011)
  • Author(s): Isao Maruyama
  • Organizer: CIFAR/MEXT Japanese Network MEETING on "Novel State of Matter Induced by Frustration"
  • Place of Presentation: Vancouver (Canada)
  • Year and Date: 2011-05-30
• [Presentation] Boundary in the Matrix Product States (2011)
  • Author(s): I. Maruyama
  • Organizer: International Workshopon Tensor Networks
  • Place of Presentation: Bribie,(Australia)
  • Year and Date: 2011-02-20
• [Presentation] Boundary in the Matr ix Product States (2011)
  • Author(s): I.Maruyama
  • Organizer: Internanal Wor kshop on Tensor Networks
  • Place of Presentation: Bribie(Australia)
  • Year and Date: 2011-02-20
• [Presentation] Boundary in the Matrix Product States (2011)
  • Author(s): I.Maruyama
  • Organizer: International Workshop on Tensor Networks
  • Place of Presentation: Bribie, (Australia)
  • Year and Date: 2011-02-20
• [Presentation] Boundary Operator in the Matrix Product States (2010)
  • Author(s): I. Maruyama
  • Organizer: Density Matrix Renormalization Group to Tensor Network Formulations
  • Place of Presentation: 京都
  • Year and Date: 2010-10-28
• [Presentation] Boundary Operator in the Matrix Product States (2010)
  • Author(s): I.Maruyama.
  • Organizer: Densi ty Matrix Renormalization Group to Tensor Network Formulations
  • Place of Presentation: 京都
  • Year and Date: 2010-10-28
• [Presentation] En tanglement Entropy and Energy Accu racy for the Small System Size : MP S, TTN, and MERA (2010)
  • Author(s): M.Orii, H.Ueda, I.Maruyama
  • Organizer: Density Matrix Renormalization Group to Tensor Ne twork Formulations
  • Place of Presentation: 京都
  • Year and Date: 2010-10-28
• [Presentation] Entanglement Entropy and Energy Accuracy for the Small System Size : MPS, TTN, and MERA (2010)
  • Author(s): M.Orii, H.Ueda, I.Maruyama
  • Organizer: Density Matrix Renormalization Group to Tensor Network Formulations
  • Place of Presentation: 京都
  • Year and Date: 2010-10-28
• [Presentation] ベーテ仮設解の行列積表示:格子系とその連続極限 (2010)
  • Author(s): 丸山勲, 桂法称
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2010-09-25
• [Presentation] 熱力学極限での一様行列積状態:フラストレートした量子スピン鎖への適用 (2010)
  • Author(s): 上田宏, 丸山勲
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2010-09-25
• [Presentation] Tree Tensor Networkにおけるエンタングルメントの評価とその改良 (2010)
  • Author(s): 折井仁嗣, 上田宏, 丸山勲
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2010-09-24
• [Presentation] Uniform Matrix Product State for Quantum Sp in Chain in the Thermodynamic Limi (2010)
  • Author(s): H.Ueda, I.Maruyama
  • Organizer: International Conference on Core Research and Engineering Science of Advanced Materials
  • Place of Presentation: 大阪
  • Year and Date: 2010-06-02
• [Presentation] Uniform Matrix Product State for Quantum Spin Chain in the Thermodynamic Limit (2010)
  • Author(s): H.Ueda, I.Maruyama
  • Organizer: International Conference on Core Research and Engineering Science of Advanced Materials
  • Place of Presentation: 大阪
  • Year and Date: 2010-06-02
• [Presentation] A New Quantum Simulation using the Entanglement Entropy (2010)
  • Author(s): M.Orii, H.Ueda, I.Maruyama
  • Organizer: International Conference on Core Research and Engineering Science of Advanced Materials
  • Place of Presentation: 大阪
  • Year and Date: 2010-06-02
• [Presentation] フラットバンド模型のトポロジカルな分類 (2009)
  • Author(s): 丸山勲, 桂法称, 田中彰則, 田崎晴明
  • Organizer: 日本物理学会
  • Place of Presentation: 熊本大学
  • Year and Date: 2009-09-28
• [Presentation] スピン1/2系におけるハルデーン相の量子化ベリー位相と断熱変形 (2008)
  • Author(s): 丸山勲
  • Organizer: 日本物理学会
  • Place of Presentation: 岩手大学
• [Remarks]
  • URL: http://researchmap.jp/i.maruyama