Exact analysis on dynamical quantum correlation functions and its applications to equilibrium and non-equilibrium systems

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K03452
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Shizuoka University
• Principal Investigator: Suzuki Junji 静岡大学, 理学部, 教授 (40222062)
• Co-Investigator(Kenkyū-buntansha): 国場 敦夫 東京大学, 大学院総合文化研究科, 教授 (70211886)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 量子相関 / 動的相関関数 / 量子転送行列法 / 完全WKB法 / 熱的形状因子展開 / 久保公式 / spin conductivity

Outline of Final Research Achievements

We establish a new framework in the exact evaluation of dynamical correlation functions of low dimensional quantum Integrable systems. This is accomplished by combining the quantum transfer matrix, the exact WKB and the thermal form factor expansion methods. By applying the framework to the prototypes of magnetic chains, we are able to study their dynamical correlation functions quantitatively. As a result, we can confirm the results obtained by an independent method (vertex operators) and go further to examine the contributions from higher excitations. The exact data on dynamical correlation functions make it possible to evaluate the transport properties of low dimensional materials directly from the celebrated Kubo formula.
As explicit example, we evaluate the dynamical form factor and the optical spin conductivity which are expected to be studied by experiments.

Free Research Field

物性基礎論、統計力学、数理物理学

Academic Significance and Societal Importance of the Research Achievements

可積分系とはいえ、既存の方法論では困難であった動的相関関数の定量的評価に対して、新しい方法論を構築することにより、久保公式になんら近似を行うことなしに、実験検証可能である輸送係数の評価が可能となった。これにより強相関系の理論と実験の間に新たな橋をかけることができた、と考えている。いまだ実験的な検証が難しいspin conductivityに対して定量的な予言を与えることで実験研究に刺激を与えることを期待している。