Quench dynamics near a quantum critical point

TL;DR

This paper investigates the scaling behavior of various physical quantities during quantum quenches near a critical point, revealing connections to susceptibilities and extending to finite temperatures with experimental relevance.

Contribution

It provides a comprehensive analysis of quench dynamics at quantum critical points, linking scaling laws to adiabatic susceptibilities and generalizing to finite temperature scenarios.

Findings

Scaling laws relate excitation probability and entropy to quench amplitude.

Fidelity susceptibility is key for sudden quenches.

Finite temperature effects influence low-energy excitation statistics.

Abstract

We study the dynamical response of a system to a sudden change of the tuning parameter $\lambda$ starting (or ending) at the quantum critical point. In particular we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning parameter, showing a close connection between the scaling behavior of these quantities with the singularities of the adiabatic susceptibilities of order $m$ at the quantum critical point, where $m$ is related to the power of the quench. Precisely for sudden quenches the relevant susceptibility of the second order coincides with the fidelity susceptibility. We discuss the generalization of the scaling laws to the finite temperature quenches and show that the statistics of the low-energy excitations becomes important. We illustrate the relevance of those results for cold atoms experiments.