Short-time universal scaling and light-cone dynamics after a quench in an isolated quantum system in $d$ spatial dimensions

TL;DR

This paper studies the universal scaling and light-cone dynamics in an isolated quantum system after a quench, using a perturbative renormalization-group approach to analyze prethermal behavior and the emergence of dissipation.

Contribution

It introduces a perturbative RG framework to analyze quench dynamics in $d>2$ dimensions, revealing universal aging and light-cone effects near criticality.

Findings

Universal aging behavior observed at the critical point.

Emergence of a light cone due to ballistic propagation of excitations.

Inelastic scattering leads to secular dissipation, signaling departure from prethermal regime.

Abstract

We investigate the effects of fluctuations on the dynamics of an isolated quantum system represented by a $\phi^4$ field theory with $O(N)$ symmetry after a quench in $d>2$ spatial dimensions. A perturbative renormalization-group approach involving a dimensional expansion in $\epsilon=4-d$ is employed in order to study the evolution within a prethermal regime controlled by elastic dephasing. In particular, we focus on a quench from a disordered initial state to the critical point, which introduces an effective temporal boundary in the evolution. At this boundary, the relevant fields acquire an anomalous scaling dimension, while the evolution of both the order parameter and its correlation and response functions display universal aging. Since the relevant excitations propagate ballistically, a light cone in real space emerges. At longer times, the onset of inelastic scattering appears as secularly growing self-generated dissipation in the effective Keldysh field theory, with the strength of the dissipative vertices providing an estimate for the time needed to leave the prethermal regime.