Scaling of the Berry Phase in the Yang-Lee Edge Singularity

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

doi:10.3390/e21090836

Abstract

We study the scaling behavior of the Berry phase in the Yang-Lee edge singularity (YLES) of the non-Hermitian quantum system. A representative model, the one-dimensional quantum Ising model in an imaginary longitudinal field, is selected. For this model, the dissipative phase transition (DPT), accompanying a parity-time (PT) symmetry-breaking phase transition, occurs when the imaginary field changes through the YLES. We find that the real and imaginary parts of the complex Berry phase show anomalies around the critical points of YLES. In the overlapping critical regions constituted by the (0 + 1)D YLES and (1 + 1)D ferromagnetic-paramagnetic phase transition (FPPT), we find that the real and imaginary parts of the Berry phase can be described by both the (0 + 1)D YLES and (1 + 1)D FPPT scaling theory. Our results demonstrate that the complex Berry phase can be used as a universal order parameter for the description of the critical behavior and the phase transition in the non-Hermitian systems.

Highlights

Motivated by the pioneering work of Berry [1], the Berry phase in quantum mechanics has become the subject of a variety of theoretical and experimental investigations
According to the hybridized Kibble-Zurek scaling (HKZS), both the (0 + 1)D Yang-Lee edge singularity (YLES) and (1 + 1)D ferromagnetic-paramagnetic phase transition (FPPT) critical theories are applicable simultaneously in this overlapping region, and the coexistence of these two scaling theories can result in a constraint on the scaling functions [27]
These results demonstrate that the behaviors of both the real and imaginary parts of the Berry phase can be well described by the usual FPPT scaling theories

Summary

Introduction

Motivated by the pioneering work of Berry [1], the Berry phase in quantum mechanics has become the subject of a variety of theoretical and experimental investigations. Besides QPT and classical phase transition, the dissipative phase transition (DPT) of the Yang-Lee edge singularity (YLES) in the non-Hermitian quantum systems has been studied [21,22,23,24,25,26,27]. Different from QPT, DPT in the non-Hermitian quantum systems is induced by changing the strength of the dissipation. Given the importance of PT symmetric quantum mechanics, it is interesting to study the scaling behaviors of the complex Berry phase in the YLES. This method is applied to a representative example, the one-dimensional quantum Ising model in an imaginary longitudinal field In this model, an overlapping region exists, which is constituted by the (0 + 1)-dimension ((0 + 1)D) YLES and the (1 + 1)D ferromagnetic-paramagnetic phase transition (FPPT) critical regions.

The Berry Phase of the One-Dimensional Quantum Ising Model in An Imaginary

Numerical Results

Summary