Algebraic approaches to strongly correlated quantum many-body systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17719
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: The University of Tokyo
• Principal Investigator: Katsura Hosho 東京大学, 大学院理学系研究科(理学部), 准教授 (80534594)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 物性基礎論 / 数理物理 / 量子多体系 / トポロジカル相 / マヨラナフェルミオン / スピン鎖 / エンタングルメント / 正弦２乗変形

Outline of Final Research Achievements

We have studied the ground-state properties of a variety of quantum many-body systems describing interacting fermions or spins, from a mathematical physics point of view. In particular, we focused on the following two aspects: (i) topological phases of systems with interaction and/or disorder, (ii) algebraic analysis of one-dimensional quantum systems with spatial modulation. In the former, we have obtained exact results for the ground states of the interacting Kitaev chain, disordered topological insulators and superconductors, and the quantum trimer model. In the latter, there was also progress in the sine-square deformation of free fermions in one-dimensional continuous space and that of conformal field theories. In addition, we obtained some results for the entanglement in the ground states of solvable spin chains.

Free Research Field

物性理論、統計力学