中国科学技术大学蔡德欢团队实现了通过动态量子相变表征经典伊辛模型的杨李零点。相关论文于2025年4月8日发表在《物理评论A》杂志上。

在量子动力学中，洛施密特振幅类似于正则系综中的配分函数。配分函数中的零表示相变，而洛施密特振幅中零的存在表示动态量子相变。基于经典量子对应关系，研究组证明了经典伊辛模型的配分函数等价于非厄米动力学中的洛施密特振幅，从而将具有可变系统大小的伊辛模型映射到非厄米力学。

因此，经典伊辛模型的杨李零点和杨李边缘奇异性分别对应于动态量子相变的临界时间和非厄米哈密顿量的异常点。该工作揭示了杨李零点和非厄米动力学之间的内在联系，为前者提供了动态表征。

附：英文原文

Title: Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions

Author: Mingtao Xu, Wei Yi, De-Huan Cai

Issue&Volume: 2025/04/08

Abstract: In quantum dynamics, the Loschmidt amplitude is analogous to the partition function in the canonical ensemble. Zeros in the partition function indicate a phase transition, while the presence of zeros in the Loschmidt amplitude indicates a dynamical quantum phase transition. Based on the classical-quantum correspondence, we demonstrate that the partition function of a classical Ising model is equivalent to the Loschmidt amplitude in non-Hermitian dynamics, thereby mapping an Ising model with variable system size to the non-Hermitian dynamics. It follows that the Yang-Lee zeros and the Yang-Lee edge singularity of the classical Ising model correspond to the critical times of the dynamic quantum phase transitions and the exceptional point of the non-Hermitian Hamiltonian, respectively. Our work reveals an inner connection between Yang-Lee zeros and non-Hermitian dynamics, offering a dynamic characterization of the former.

DOI: 10.1103/PhysRevA.111.042204

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.042204