Out-of-equilibrium dynamics of the XY spin chain from form factor expansion

TL;DR

This paper develops a unified framework using form factor expansion to compute correlation functions in the out-of-equilibrium XY spin chain with time-dependent parameters, providing exact results for several key observables.

Contribution

It introduces the Coherent Ensemble as a natural class of states and derives exact out-of-equilibrium expressions for correlation functions using Fredholm determinants.

Findings

Exact expressions for order parameter one-point function

Exact dynamical two-point function

Exact equal-time three-point function

Abstract

We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides a natural and unified framework for out-of-equilibrium physics in this model. We show that $all$ correlation functions in the CE can be computed using form factor expansion and expressed in terms of Fredholm determinants. In particular, we present exact out-of-equilibrium expressions in the thermodynamic limit for the previously unknown order parameter one-point function, dynamical two-point function and equal-time three-point function.