Signature of nonequilibrium quantum phase transition in the long time average of Loschmidt echo

TL;DR

This paper shows that nonanalyticities in the long time average of Loschmidt echo can identify nonequilibrium quantum phase transitions, providing a new way to characterize these transitions beyond dynamical quantum phase transitions.

Contribution

It introduces the long time average of Loschmidt echo as a novel indicator for nonequilibrium quantum phase transitions, linking it to rate functions and fidelity susceptibility.

Findings

Nonanalyticities in long time average signal phase transitions.

Sharp changes or divergences in rate functions occur at critical points.

Connection established between rate function derivatives and fidelity susceptibility.

Abstract

We unveil the role of the long time average of Loschmidt echo in the characterization of nonequilibrium quantum phase transitions by studying sudden quench processes across quantum phase transitions in various quantum systems. While the dynamical quantum phase transitions are characterized by the emergence of a series of zero points at critical times during time evolution, we demonstrate that nonequilibrium quantum phase transitions can be identified by nonanalyticities in the long time average of Loschmidt echo. The nonanalytic behaviours are illustrated by a sharp change in the long time average of Loschmidt echo or the corresponding rate function or the emergence of divergence in the second derivative of rate function when the driving quench parameter crosses the phase transition points. The connection between the second derivative of rate function and fidelity susceptibility is also discussed.