Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems

TL;DR

This paper demonstrates how Yang-Lee edge singularities, as many-body exceptional points, can be observed in non-Hermitian systems through Loschmidt echoes, revealing critical behavior and exponents consistent with nonunitary conformal field theory.

Contribution

It introduces a method to observe Yang-Lee edge singularities in non-Hermitian many-body systems using Loschmidt echoes, linking nonunitary dynamics to critical phenomena.

Findings

Loschmidt echoes show distinct dynamics in $ ext{PT}$-symmetric and broken regimes.

Exceptional points are identified in non-Hermitian Ising and Yang-Lee models.

Critical exponents match predictions from nonunitary conformal field theory.

Abstract

The Yang-Lee edge singularity is an intriguing critical phenomenon characterized by nonunitary field theory. However, its experimental realization for interacting many-body systems remains elusive. We show that Yang-Lee edge singularities, regarded as many-body exceptional points, can be observed using both the self-normal and the associated-biorthogonal Loschmidt echoes, leveraging the advantages of nonunitary dynamics in non-Hermitian systems. The Loschmidt echoes are demonstrated to display unitary dynamics in the $\mathcal{PT}$-symmetric regime but exhibit nonunitary dynamics in the $\mathcal{PT}$ symmetry-broken regime, leading to a sharp change near an exceptional point. We hereby identify exceptional points in both the non-Hermitian transverse field Ising model and the Yang-Lee model, and determine the critical exponent that is consistent with nonunitary conformal field theory. This work provides a direct observation of Yang-Lee edge singularities in non-Hermitian many-body systems arising from nonunitary dynamics.