Study of topological order and entanglement in strongly correlated quantum spin systems

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K05564
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: The University of Tokyo
• Principal Investigator: Todo Synge 東京大学, 大学院理学系研究科(理学部), 教授 (10291337)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: トポロジカル秩序 / エンタングルメントエントロピー / 臨界現象 / 計算物理 / テンソルネットワーク / 量子モンテカルロ法 / 量子スピン系 / 量子ダイマー模型

Outline of Final Research Achievements

In order to characterize the various quantum states in quantum spin systems and the novel quantum phase transitions between these quantum phases, we have developed various numerical methods based on quantum Monte Carlo and tensor network methods. Although the quantities characterizing the topological order have been studied mainly for one-dimensional quantum systems, precise and efficient measurements are now possible for higher-dimensional systems. Using the developed method, we carried out large-scale simulations to analyze the phase transition of the topological phase field. We have also developed and released software based on the new algorithm.

Free Research Field

計算物理・物性理論

Academic Significance and Societal Importance of the Research Achievements

トポロジカルな秩序やトポロジカルな励起は、エキゾチックな相転移現象や非自明な量子状態において非常に大きな役割を果たしており、その理解は学術的にも新しい量子技術の発展のためにも重要である。本研究で開発された、量子モンテカルロ法やテンソルネットワーク法に基づくさまざまな新規手法は、この分野の今後の研究に大きな波及効果が期待される。