Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model

TL;DR

This paper investigates non-Hermitian extensions of the XY spin chain, revealing how non-Hermiticity influences phase transitions, topological properties, and critical behavior through analytical and numerical methods.

Contribution

It provides analytical solutions linking quasienergies and topological invariants in non-Hermitian XY models, and explores their critical phenomena and phase transitions.

Findings

Non-Hermiticity induces a new universality class with unusual critical exponents.

Entanglement transition coincides with topological phase transition.

Loschmidt echo effectively characterizes phase transitions in non-Hermitian systems.

Abstract

In this work we study non-Hermitian extensions of the paradigmatic spin-1/2 XY chain in a magnetic field. Using the mapping of the model to free fermion form, we provide analytical insights into the energy spectrum of the non-Hermitian model and establish an intrinsic connection between the quasienergies and topological invariants. We also use exact diagonalization as a supplementary method to examine the performance of biorthogonal-based expectation values. Our results confirm that the theoretical analysis is consistent with the numerical results, with the extended phase diagram determined via the analytical solution and the critical behavior of the fidelity and entanglement. The entanglement transition goes hand in hand with the non-Hermitian topological phase transition. Like the Hermitian case, we analyze the critical behavior using finite-size scaling. Our results show that non-Hermiticity can induce the system into a new universality class with unusual critical exponent. We also emphasize the ability of the Loschmidt echo to characterize potential phase transitions and introduce the average of the Loschmidt echo to describe phase transitions in non-Hermitian systems.