Matrix Product States of Quantum Systems on Higher Dimensional Lattices

• Project/Area Number: 24654042
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Kyushu University
• Principal Investigator: MATSUI Taku 九州大学, 数理(科)学研究科(研究院), 教授 (50199733)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 量子スピン系 / 関数解析 / 基底状態 / エンタングルメント・エントロピー / 行列積状態 / PEP状態 / split property / entanglement entropy

Outline of Final Research Achievements

(i) We considered 2dim (infinite) quantum spin systems and obtain PEPS representations for any translationally invariant states using using representations of a quadruplet of Cuntz algebras. Our construction is a generalization of the correspondence of Cuntz algebras and matrix product states in 1 dim quantum systems.(ii) We obtained a class of formal Hamiltonians for Bosonic systems on lattices for which frustration free ground states exist.

Research Products

• [Journal Article] BOUNDEDNESS OF ENTANGLEMENT ENTROPY AND SPLIT PROPERTY OF QUANTUM SPIN CHAINS (2013)
  • Author(s): 松井卓
  • Journal Title: Reviews in Mathmatical Physics Volume: 25-9 Issue: 09 Pages: 1-31
  • DOI: 10.1142/s0129055x13500189
  • Peer Reviewed
• [Journal Article] Kakutani dichotomy on free states. (2012)
  • Author(s): Taku Matsui, SHigeru Yamagami
  • Journal Title: Letters in Mathematical Physics Volume: 102
  • Peer Reviewed
• [Presentation] On frustration Free Ground States (2015)
  • Author(s): 松井卓
  • Organizer: QI work shop 2015
  • Place of Presentation: 国立情報学研究所
  • Year and Date: 2015-02-18
• [Presentation] 量子系の matrix product state をめぐって (2014)
  • Author(s): 松井卓
  • Organizer: 作用素論・作用素環論研究集会
  • Place of Presentation: 東洋大学
  • Year and Date: 2014-12-26
• [Presentation] レゾルベント代数とボーズ粒子系の統計力学 (2014)
  • Author(s): 松井卓
  • Organizer: 量子場の数理とその周辺
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-10-08
• [Book] 作用素環と無限量子系 (2014)
  • Author(s): 松井卓
  • Total Pages: 152
  • Publisher: サイエンス社