Loschmidt Echo Revivals: Critical and Noncritical

TL;DR

This paper investigates the behavior of Loschmidt echo revivals in quantum systems, introducing a new exactly solvable model and analyzing conditions for revivals, challenging previous assumptions about their relation to quantum critical points.

Contribution

The study presents an exactly solvable extended Su-Schrieffer-Heeger model and clarifies conditions for Loschmidt echo revivals, providing a counterexample to existing beliefs.

Findings

Loschmidt echo revivals are not always linked to quantum critical points

The extended SSH model exhibits non-revival dynamics under certain conditions

Conditions for periodic revivals are identified through analysis of the XY model

Abstract

A quantum phase transition is generally thought to imprint distinctive characteristics on the nonequilibrium dynamics of a closed quantum system. Specifically, the Loschmidt echo after a sudden quench to a quantum critical point $-$ measuring the time dependence of the overlap between initial and time-evolved states $-$ is expected to exhibit an accelerated relaxation followed by periodic revivals. We here introduce a new exactly solvable model, the extended Su-Schrieffer-Heeger model, the Loschmidt echo of which provides a counterexample. A parallell analysis of the quench dynamics of the three-site spin-interacting $XY$ model allows us to pinpoint the conditions under which a periodic Loschmidt revival actually appears