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

TL;DR

This paper establishes a connection between the Yang-Lee zeros of the classical Ising model and dynamical quantum phase transitions via non-Hermitian quantum dynamics, revealing a new perspective on phase transition characterization.

Contribution

It demonstrates that the Yang-Lee zeros of the classical Ising model correspond to critical times in non-Hermitian quantum dynamics, linking classical phase transitions to quantum dynamical phenomena.

Findings

Yang-Lee zeros map to critical times of dynamical quantum phase transitions

Yang-Lee edge singularity corresponds to exceptional points in non-Hermitian Hamiltonians

Provides a dynamic framework to characterize classical phase transitions

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.