Exact results for the criticality of quench dynamics in quantum Ising models

TL;DR

This paper provides exact analytical results for the critical behavior of quench dynamics in the quantum Ising model, revealing how susceptibility features signal quantum phase transitions at both zero and finite temperatures.

Contribution

It offers the first exact analysis of quench dynamics in the quantum Ising model, demonstrating the robustness of susceptibility discontinuities at the critical point across temperatures.

Findings

Quench magnetic susceptibility mirrors static susceptibility scaling.

Discontinuity in susceptibility persists at the quantum critical point.

Robustness of critical signatures at finite temperatures.

Abstract

Based on the obtained exact results we systematically study the quench dynamics of a one-dimensional spin-1/2 transverse field Ising model with zero- and finite-temperature initial states. We focus on the magnetization of the system after a sudden change of the external field and a coherent time-evolution process. With a zero-temperature initial state, the quench magnetic susceptibility as a function of the initial field strength exhibits strongly similar scaling behaviors to those of the static magnetic susceptibility, and the quench magnetic susceptibility as a function of the final field strength shows a discontinuity at the quantum critical point. This discontinuity remains robust and always occurs at the quantum critical point even for the case of finite-temperature initial systems, which indicates a great advantage of employing quench dynamics to study quantum phase transitions.