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

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 1-point function, dynamical 2-point function and equal-time 3-point function.

Automated summary

We study the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. By considering a particular subset of Gaussian states called Coherent Ensemble (CE), we propose a natural and unified framework for describing out-of-equilibrium physics in this model. We establish that all correlation functions in the CE can be computed using form factor expansion and are expressible in terms of Fredholm determinants. Specifically, we derive exact out-of-equilibrium expressions in the thermodynamic limit for the previously unknown order parameter 1-point function, dynamical 2-point function, and equal-time 3-point function.