Dynamics of integrable spin chains with non-Hermitian conserved quantities

2023 Fiscal Year Final Research Report

• Project/Area Number: 18K13465
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: The University of Tokyo
• Principal Investigator: Matsui Chihiro 東京大学, 大学院数理科学研究科, 准教授 (60732451)
• Project Period (FY): 2018-04-01 – 2024-03-31
• Keywords: 統計力学 / 量子可積分系 / 量子スピン系

Outline of Final Research Achievements

The aim of this study is to investigate the effect of quantum integrability on the physical behavior of systems in non-equilibrium states, and the following results were obtained: (1)For the anisotropic Heisenberg spin chain, we constructed quasi-local and spin-reversal asymmetric conserved quantities. (2) We demonstrated that the behavior of the anisotropic Heisenberg spin chain in a non-equilibrium steady state can be characterized by the linearly independent conserved quantities constructed in (1). (3) For an open system with dissipation at both ends of the anisotropic Heisenberg spin chain, we investigated how integrability affects the behavior of the current in the steady state. In particular, we showed that the spin current in the solvable steady state is not affected by impurities in the bulk.

Free Research Field

数理物理学

Academic Significance and Societal Importance of the Research Achievements

近年，固有状態熱化仮説により熱平衡化のメカニズムが飛躍的に解明されつつある一方，量子可積分系は固有状態熱化仮説の反例として注目を集めている．可積分系は多数の保存量の存在により熱平衡化が起こらず，統計力学が適用できない対象であるが，一方で可積分性により物理量の厳密な計算が可能である．このことは，可積分系が統計力学を非平衡定常状態へと拡張する際のベンチマークとなりうることを示唆している．また，可積分系が長時間で到達する非平衡定常状態は，非零なカレントの存在を特徴とし，駆動を必要とせず半恒久的にカレントを保ち続けるデバイスの開発への応用が期待できる．