Pseudo-Yang-Lee Edge Singularity Critical Behavior in a Non-Hermitian Ising Model.

Liang-Jun Zhai,Huai-Yu Wang,Guang-Yao Huang

doi:10.3390/e22070780

Abstract

The quantum phase transition of a one-dimensional transverse field Ising model in an imaginary longitudinal field is studied. A new order parameter M is introduced to describe the critical behaviors in the Yang-Lee edge singularity (YLES). The M does not diverge at the YLES point, a behavior different from other usual parameters. We term this unusual critical behavior around YLES as the pseudo-YLES. To investigate the static and driven dynamics of M, the (1+1) dimensional ferromagnetic-paramagnetic phase transition ((1+1) D FPPT) critical region, (0+1) D YLES critical region and the (1+1) D YLES critical region of the model are selected. Our numerical study shows that the (1+1) D FPPT scaling theory, the (0+1) D YLES scaling theory and (1+1) D YLES scaling theory are applicable to describe the critical behaviors of M, demonstrating that M could be a good indicator to detect the phase transition around YLES. Since M has finite value around YLES, it is expected that M could be quantitatively measured in experiments.

Highlights

As one of the most interesting phenomena in many body systems, quantum phase transition occurs when parameters of a system change through a critical point, and the occurrence indicates the emergence of new physics and new states of the system [1,2]
Interesting characters have been found in various non-Hermitian systems, such as the parity-time (PT) symmetry breaking phase transition induced by interface state [18,19] and the real-complex energy spectrum transition accompanied by a many-body localization-delocalization phase transition [20]
It was found that the Kibble-Zurek scaling (KZS) mechanism was still applicable in describing the driven dynamics across the exceptional points (EPs), where the complex spectrum becomes gapless [21]

Summary

Introduction

As one of the most interesting phenomena in many body systems, quantum phase transition occurs when parameters of a system change through a critical point, and the occurrence indicates the emergence of new physics and new states of the system [1,2]. Interesting characters have been found in various non-Hermitian systems, such as the parity-time (PT) symmetry breaking phase transition induced by interface state [18,19] and the real-complex energy spectrum transition accompanied by a many-body localization-delocalization phase transition [20]. We are going to define a new order parameter, which is not diverged at the YLES point, to character the critical behaviors around the YLES for the non-Hermitian Ising model. This order parameter obeys the similar scaling behavior with the usual order parameter but the critical exponent σ is positive.

The Non-Hermitian Ising Model and Order Parameter

Pseudo-YLES Critical Behaviors

Summary