Optimization of tensor network state using higher order singular value decomposition

2017 Fiscal Year Final Research Report

• Project/Area Number: 25800221
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Institute of Physical and Chemical Research (2013-2014, 2016-2017); Meiji University (2015)
• Principal Investigator: Ueda Hiroshi 国立研究開発法人理化学研究所, 計算科学研究機構, 研究員 (40632758)
• Research Collaborator: NISHINO Tomotoshi 神戸大学, 理学研究科, 准教授 (00241563) ; OKUNISHI Kouichi 新潟大学, 自然科学系, 准教授 (30332646) ; Maruyama Isao 福岡工業大学, 情報工学部, 准教授 (20422339)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 密度行列繰り込み群 / テンソルネットワーク / 量子スピン系 / 古典スピン系 / 量子相転移 / スケーリング解析 / 高次特異値分解 / 量子古典対応

Outline of Final Research Achievements

The tensor network method is an extension of the matrix product method, which is a powerful tool to analyze one-dimensional quantum / two-dimensional classical multi-body systems, and is applicable for high dimensional systems. In this study, through the sophistication of the tensor network method, we have succeeded in "Structural analysis of the entanglement spectrum in the tensor renormalization group using the higher-order singular value decomposition","Identification of symmetry-protected topological phases in one-dimensional frustrated quantum spin systems and SU(n)[n = 3 and 4] spin systems "," Development of the exact diagonalization method adapted the symmetry of real space and spin space which is specialized for calculating low-energy states in the vicinity of saturation field", and "Generalization of entanglement scaling analysis using the corner transfer-matrix renormalization group method".

Free Research Field

計算物理