The relation between degree of freedom of spin chains and supersymmetry emerging in their effective field theories

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K20939
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics; Particle/Nuclear/Cosmic ray/Astro physics
• 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): 2015-04-01 – 2019-03-31
• Keywords: 可積分系 / 量子スピン鎖 / 超対称性 / 非平衡系

Outline of Final Research Achievements

We aimed to investigate (1) the relation between the degree of freedom in higher-spin integrable spin chains and the supersymmetry emerging in their effective field theories, and (2) various physics related to spin chains. In order to achieve these aims, we worked on the following projects:
We have showed that the hidden supersymmetry behind spin chains corresponds to the supersymmetry of their effective field theories by using the fact that the scattering matrix of an integrable spin chain coincides with that of its effective field theory. We have also discussed non-equilibrium phenomena including the characterizing behavior of classical stochastic processes with multi-degree of freedom associated with higher-spin systems and the steady state of anisotropic spin chain with both ends attached to spin baths.

Free Research Field

物理学

Academic Significance and Societal Importance of the Research Achievements

有効場理論を用いたスピン鎖の解析は量子一次元物理系の重要な中核を成すが，スピン鎖のような離散系ではサイト数に応じて許される励起状態が異なるため，連続系との対応を議論する際には注意が必要である．本研究成果は，離散系と連続系に共通の励起構造を用いて解析を行なったという点で，両者の対応関係を提示し，離散系における隠れた対称性の理解を前進させるものである．
また，多自由度な古典確率過程やスピン浴に接した量子スピン鎖など，量子スピン鎖に関連した非平衡現象の解明により，量子スピン鎖の可積分性や多自由度への拡張のしやすさが関連する非平衡系における多彩な物理を調べるのに有効であることを示した．