Quantum Quench in the Transverse Field Ising Chain

TL;DR

This paper analyzes the non-equilibrium dynamics of the transverse field Ising chain after a sudden quench, providing exact results for correlation functions and demonstrating the emergence of a generalized Gibbs ensemble.

Contribution

It offers the first exact analytical characterization of post-quench correlation functions in the TFIC and confirms the GGE as the description of the stationary state.

Findings

Stationary two-point correlation functions are described by a GGE.

The approach to equilibrium can be explained by GGE dynamics.

Exact asymptotic formulas for correlation functions are derived.

Abstract

We consider the time evolution of observables in the transverse field Ising chain (TFIC) after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.