Geometric phase and phase diagram for non-Hermitian quantum XY model

TL;DR

This paper investigates the geometric phase and phase diagram of a non-Hermitian quantum XY model, revealing how the Berry curvature divergence marks symmetry-breaking boundaries and analyzing scaling behaviors analytically.

Contribution

It provides an exact solution-based analysis of the geometric phase and phase diagram in a non-Hermitian quantum XY model, highlighting the relation between Berry curvature divergence and symmetry boundaries.

Findings

Full real spectrum in multiple regions for finite size system

Phase boundary corresponds to divergence of Berry curvature

Analytical scaling behaviors of ground state energy and Berry curvature

Abstract

We study the geometric phase for the ground state of a generalized one-dimensional non-Hermitian quantum XY model, which has transverse-field-dependent intrinsic rotation-time reversal symmetry. Based on the exact solution, this model is shown to have full real spectrum in multiple regions for the finite size system. The result indicates that the phase diagram or exceptional boundary, which separates the unbroken and broken symmetry regions corresponds to the divergence of the Berry curvature. The scaling behaviors of the groundstate energy and Berry curvature are obtained in an analytical manner for a concrete system.