Signature of quantum phase transition manifested in quantum fidelity at finite temperature

TL;DR

This paper demonstrates that a quantum fidelity-based rate function can reveal signatures of quantum phase transitions at finite temperatures, extending the detection capabilities beyond low-temperature regimes and connecting to dynamical quantum phase transitions.

Contribution

The authors develop and analyze a quantum fidelity-derived rate function that detects quantum criticality at finite temperatures across various many-body systems, linking it to dynamical quantum phase transitions.

Findings

Rate function exhibits nonanalyticity at quantum critical points at finite temperature.

The rate function reduces to that used in dynamical quantum phase transition studies at zero temperature.

Long-time behavior of the rate function can identify equilibrium quantum phase transitions.

Abstract

The signature of quantum phase transition is generally wiped out at finite temperature. A few quantities that have been observed to carry this signature through a nonanalytic behavior are also limited to low temperatures only. With an aim to identify a suitable dynamical quantity at a high temperature, we have recently constructed a function from quantum fidelity, which has the potential to bear a nonanalytic signature at the quantum critical point beyond low temperature regime. In this paper, we elaborate our earlier work and demonstrate the behavior of the corresponding rate function and the robustness of the nonanalyticity for a number of many-body Hamiltonians in different dimensions. We have also shown that our rate function reduces to that used in the demonstration of the dynamical quantum phase transition (DQPT) at zero temperature. It has been further observed that, unlike DQPT, the long time limit of the rate function can faithfully detect the equilibrium quantum phase transition as well.