Exceptional points near first- and second-order quantum phase transitions

TL;DR

This paper investigates how the distribution of exceptional points in the complex parameter domain reflects the nature of quantum phase transitions, providing a signature of criticality that is independent of specific parameters.

Contribution

It demonstrates that the distribution of exceptional points near quantum critical points reveals the type of phase transition and remains robust under random perturbations.

Findings

EPs approach critical points exponentially or polynomially depending on the transition order

EP distribution near critical points encodes information about QPT type

EP distribution serves as a parameter-independent signature of quantum criticality

Abstract

We study impact of quantum phase transitions (QPTs) on the distribution of exceptional points (EPs) of the Hamiltonian in complex-extended parameter domain. Analyzing first- and second-order QPTs in the Lipkin model, we find an exponentially and polynomially close approach of EPs to the respective critical point with an increasing size of the system. If the critical Hamiltonian is subject to random perturbations of various kinds, the averaged distribution of EPs close to the critical point still carries decisive information on the QPT type. We therefore claim that properties of the EP distribution represent a parametrization-independent signature of criticality in quantum systems.