Finite-temperature quantum criticality in a complex-parameter plane

TL;DR

This paper investigates finite-temperature quantum criticality in a non-Hermitian PT-symmetric Ising model, extending fidelity-based detection methods to complex parameters and providing exact eigenstates for analysis.

Contribution

It introduces the complete set of eigenstates for a non-Hermitian Ising model and demonstrates the extension of fidelity approach to finite-temperature quantum phase transitions in such systems.

Findings

Fidelity approach can detect finite-temperature QPT in non-Hermitian systems

Exact eigenstates of the non-Hermitian Hamiltonian are derived

Finite-temperature quantum criticality can be explored in a complex-parameter plane

Abstract

A conventional quantum phase transition (QPT) occurs not only at zero temperature, but also exhibits finite-temperature quantum criticality. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the finite-temperature quantum criticality in a non-Hermitian PT -symmetric Ising model. We present the complete set of exact eigenstates of the non-Hermitian Hamiltonian, based on which the mixed-state fidelity in the context of biorthogonal bases is calculated. Analytical and numerical results show that the fidelity approach to finite-temperature QPT can be extended to the non-Hermitian Ising model. This paves the way for experimental detection of quantum criticality in a complex-parameter plane.