Detection of quantum phase boundary at finite temperatures in integrable spin models

TL;DR

This paper identifies a physical quantity, related to quantum fidelity, that exhibits non-analytic behaviour at finite temperatures across quantum phase transitions in integrable spin models, providing a new way to detect such transitions.

Contribution

It introduces a method to detect quantum phase boundaries at finite temperatures using a non-analytic quantity derived from quantum fidelity, applicable to various integrable models.

Findings

Analytic results for XY chain and 2D Kitaev model.

Numerical results for 3D Weyl semimetal Hamiltonian.

Identification of non-analytic behaviour at finite temperatures.

Abstract

Quantum phase transitions occur when quantum fluctuation destroys order at zero temperature. With an increase in temperature, normally the thermal fluctuation wipes out any signs of this transition. Here we identify a physical quantity that shows non-analytic behaviour at finite temperatures, when an interaction parameter is quenched across the line of quantum phase transition. This quantity under consideration is the long time limit of a form of quantum fidelity. Our treatment is analytic for XY chain and 2D Kitaev model and is numerical for a 3D Hamiltonian applicable to Weyl semimetals.