Dynamical Correlations after a Quantum Quench

TL;DR

This paper demonstrates that in integrable models, dynamic correlation functions after a quantum quench relax to stationary values described by a generalized Gibbs ensemble, extending the understanding of relaxation beyond static correlations.

Contribution

It establishes that dynamic correlations after a quantum quench are governed by the same ensemble as static correlations, and derives explicit results for the transverse field Ising chain.

Findings

Dynamic correlations relax to GGE predictions.

Fluctuation dissipation theorem holds in the GGE context.

Explicit expressions for dynamic correlators in the TFIC are obtained.

Abstract

In many integrable models static (equal time) correlation functions of local observables after a quantum quench relax to stationary values, which are described by a generalized Gibbs ensemble (GGE). Here we establish that the same holds true for dynamic (non equal time) correlation functions. More generally we show that in the absence of long-range interactions in the final Hamiltonian, the dynamics is determined by the same ensemble that describes static correlations. When the latter is a GGE the basic form of the fluctuation dissipation theorem holds, although the absorption and emission spectra are not simply related as in the thermal case. For quenches in the transverse field Ising chain (TFIC) we derive explicit expressions for the time evolution of dynamic order parameter correlators after a quench.