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arXiv · 2412.07800

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

Mingtao Xu·Wei Yi·De-Huan Cai
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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.

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Mingtao Xu, Wei Yi, De-Huan Cai. 2024-12-08. Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions. https://doi.org/10.1103/physreva.111.042204

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