Quantum Monte Carlo study on quantum magnets based on Majorana fermion representations

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K03447
• 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: The University of Tokyo
• Principal Investigator: Yasuyuki Kato 東京大学, 大学院工学系研究科(工学部), 助教 (50708534)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: 量子スピン系 / 量子モンテカルロ法 / 量子スピン液体

Outline of Final Research Achievements

We applied the Lefschetz thimble method recently developed in the field of particle physics for the negative-sign free quantum Monte Carlo simulation to the Kitaev model hosting a quantum spin liquid, which is one of the central topics of condensed matter physics. As a result, we successfully clarified the practical mitigation of the negative sign problem. Furthermore, for theoretical models of various magnetic materials, we chose an appropriate method from the quantum Monte Carlo method, the exact diagonalization, the mean field theory, the saddle point method, etc., and implemented numerical calculations. These calculations provided new insights into various focused topics such as chiral spin liquid, magnon Efimov effect, fractional corner magnetization, magnetic hedgehog lattice, and magnetoelectric effect of chiral antiferromagnets.

Free Research Field

物性II

Academic Significance and Societal Importance of the Research Achievements

本研究課題の成果は量子多体問題に対する基礎的な知見を与えるものであり，磁性体を中心に非自明な物性を予測説明するものである．特に手法開発に主眼をおいており，長年の物理学の未解決問題である量子多体系のシミュレーションの負符号問題を軽減する新手法として素粒子物理学の分野で精力的に研究が進められているレフシッツシンブル法を，近年の物性物理学の中心的関心事の一つであるキタエフスピン液体の問題に適用する方法を示し実装した．