Anomalous Spontaneous Symmetry Breaking in non-Hermitian Systems with Biorthogonal Z2-symmetry

TL;DR

This paper extends Landau's symmetry breaking theory to non-Hermitian systems, revealing a novel quantum phase transition characterized by symmetry breaking without gap closing, demonstrated through theoretical analysis and numerical results.

Contribution

It introduces a universal framework for spontaneous symmetry breaking in non-Hermitian systems with biorthogonal Z2 symmetry, uncovering a new type of phase transition.

Findings

Symmetry breaking can occur without gap closing in non-Hermitian systems.

Numerical results confirm the theoretical prediction of anomalous phase transition.

The study provides insights into universal features of non-Hermitian many-body systems.

Abstract

Landau's spontaneous symmetry breaking theory is a fundamental theory that describes the collective behaviors in many-body systems. It was well known that for usual spontaneous symmetry breaking in Hermitian systems, the order-disorder phase transition with gap closing and spontaneous symmetry breaking occur at the same critical point. In this paper, we generalized the Landau's spontaneous symmetry breaking theory to the cases in non-Hermitian (NH) many-body systems with biorthogonal Z2 symmetry and tried to discover certain universal features. We were surprised to find that the effect of the NH terms splits the spontaneous biorthogonal Z2 symmetry breaking from a (biorthogonal) order-disorder phase transition with gap closing. The sudden change of similarity for two degenerate ground states indicates a new type of quantum phase transition without gap closing accompanied by spontaneous biorthogonal Z2 symmetry breaking. We will take the NH transverse Ising model as an example to investigate the anomalous spontaneous symmetry breaking. The numerical results were consistent with the theoretical predictions.