Quantum Quenches to a Critical Point in One Dimension: some further results

TL;DR

This paper explores the dynamics of quantum quenches near critical points in one dimension, revealing thermalization, generalized Gibbs states, and effects of dispersion and scattering on propagation and horizon broadening.

Contribution

It extends previous work by analyzing initial state deformations, non-integrable effects, and their impact on quantum quench dynamics in 1+1D CFTs.

Findings

Reduced density matrices approach thermal states inside the horizon

Deformations lead to generalized Gibbs ensembles with possible parafermionic charges

Dispersion and scattering cause propagation speed dependence and horizon broadening

Abstract

We describe several results concerning global quantum quenches from states with short-range correlations to quantum critical points whose low-energy properties are described by a 1+1-dimensional conformal field theory (CFT), extending the work of Calabrese and Cardy (2006): (a) for the special class of initial states discussed in that paper we show that, once a finite region falls inside the horizon, its reduced density matrix is exponentially close in $L_2$ norm to that of a thermal Gibbs state; (b) small deformations of this initial state in general lead to a (non-Abelian) generalized Gibbs distribution (GGE) with, however, the possibility of parafermionic conserved charges; (c) small deformations of the CFT, corresponding to curvature of the dispersion relation and (non-integrable) left-right scattering, lead to a dependence of the speed of propagation on the initial state, as well as diffusive broadening of the horizon.