Survival of Hermitian Criticality in the Non-Hermitian Framework

TL;DR

This paper demonstrates that Hermitian criticality features persist in a non-Hermitian quantum model, revealing new topological and symmetry properties in open quantum systems.

Contribution

It shows that key phase transition characteristics of the Hermitian XY model are preserved in a non-Hermitian setting, with novel topological and symmetry insights.

Findings

Correlation functions and entanglement entropy scale as in Hermitian models.

Hermitian phase transition features are maintained due to symmetry behaviors.

The Luttinger liquid phase exhibits nontrivial topology characterized by winding number.

Abstract

In this work, we investigate many-body phase transitions in a one-dimensional anisotropic XY model subject to a complex-valued transverse field. Within the biorthogonal framework, we calculate the ground-state correlation functions and entanglement entropy, confirming that their scaling behavior remains identical to that in the Hermitian XY model. The preservation of Hermitian phase transition features in the non-Hermitian setting is rooted in the persistence and emergence of symmetries and their breaking. Specifically, the ferromagnetic (FM) phase arises from the breaking of a $Z_2$ symmetry, while the Luttinger liquid (LL) phase is enabled by the emergence of a $U(1)$ symmetry together with the degeneracy of the real part of the energy spectrum. The nontrivial topology of the LL phase are characterized by the winding number around the exceptional point (EP). Given that non-Hermitian systems are inherently open, this research opens a new avenue for exploring conventional quantum phase transitions that are typically vulnerable to decoherence and environmental disruption in open quantum systems.