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

2010 Fiscal Year Self-evaluation Report

• 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 Osaka University, 基礎工学研究科, 特任助教(常勤) (20422339)
• Project Period (FY): 2008 – 2011
• 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

Research Abstract

近年物性に応用されている「量子絡み合い」と「幾何学的位相」という概念を用いて、数値計算手法の一つである「密度行列繰り込み群法」を発展させるという研究計画を達成するため、これら三つのキーワードを融合した研究を進める。

Research Products

• [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 Pages: 023001-1-023001-4
  • 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 Pages: 57007-1-57007-6
  • 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 Pages: 073002-1-073002-4
  • 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 Pages: 175003-1-175003-19
  • 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 Pages: 115107-1-115107-5
  • 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 Pages: 012052-1-012052-4
  • Peer Reviewed
• [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 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] 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] 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