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

2011 Fiscal Year Final Research 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 大阪大学, 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

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 Pages: 043001-(1-4)
  • 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 Pages: 165132-(1-8)
  • 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 Pages: 20003-(1-5)
  • 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 Pages: 023001-1-4
  • 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: Europhys. Lett. Volume: 91 Pages: 57007-1-6
  • 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. Volume: 79 Pages: 073002-1-4
  • Peer Reviewed
• [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] 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] 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] 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 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
• [Remarks]
  • URL: http://researchmap.jp/i.maruyama