Quench dynamics near a quantum critical point

TLDR

The study investigates the dynamical response of a system to sudden changes of the tuning parameter λ at a quantum critical point. The authors analyze how excitation probability, quasiparticle number, heat, and entropy scale with quench amplitude, system size, and time dependence, linking these scalings to singularities of adiabatic susceptibilities and extending the analysis to finite temperatures. For sudden quenches, the second‑order susceptibility equals the fidelity susceptibility, and the scaling laws are relevant for cold‑atom experiments, with low‑energy excitation statistics playing a key role at finite temperatures.

Abstract

We study the dynamical response of a system to a sudden change of the tuning parameter $\ensuremath{\lambda}$ 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-atom experiments.