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