Dynamics of coherence: Maximal quantum Fisher information vs. Loschmidt echo

TL;DR

This paper investigates the dynamics of maximal quantum Fisher information after sudden quenches in the transverse-field Ising model, revealing universal revival times, critical behaviors at quantum phase transitions, and signatures of nonequilibrium quantum phase transitions.

Contribution

It introduces the concept of dynamical MQFI transitions, linking MQFI dynamics to quantum critical points and phase transitions, and explores their universal and critical properties.

Findings

Revival times are universal and independent of initial conditions.

Dynamical MQFI transitions occur at critical times during quenches crossing QCP.

MQFI dynamics reveal signatures of nonequilibrium quantum phase transitions.

Abstract

We consider the dynamics of maximal quantum Fisher information (MQFI) after sudden quenches for the one-dimensional transverse-field Ising model. Our results show, the same as Loschmidt echo, there is a universality for the revival times i.e., they do not depend on the initial state and the size of the quench and are given by integer multiples of $T_{rev} \simeq \frac{N}{2v_{max }}$, where $N$ is the system size and $v_{max }$ is the maximal group velocity of quasiparticles. Critically enhanced and decreased at revival and decay times as $T_{rev} \equiv T_{dec} $ are characterized by quenching from the order and disorder phases into the quantum phase transition respectively, that can be utilized to detect the quantum critical point (QCP). In some quenches crossed from the QCP, nonanalytic behaviors appear at some times due to the turning of the local observable from one direction to another because of identifying the maximum value. We name this phenomenon \textit{the dynamical MQFI transitions}, occurring at the critical times $t_c$. Interestingly, although no Fisher zero exists in the dynamics of MQFI, the first critical time emerged from the dynamical quantum phase transition is equal to the first time whose the logarithm of MQFI is minimum. In addition, we unveil the long-time run of MQFI indicates a signature of a nonequilibrium quantum phase transition at the QCP. We also discuss the probability of arising of macroscopic superpositions in the nonequilibrium dynamics of the system.