Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field

TL;DR

This paper provides exact analytic results for the time evolution of entanglement entropy in the XY chain after a quantum quench, revealing linear growth and saturation behaviors.

Contribution

It introduces a novel analytic approach using Toeplitz matrices and phase methods to study entanglement dynamics in the XY chain for arbitrary quenches.

Findings

Entanglement entropy grows linearly with time after a quench.

Saturation of entanglement entropy occurs at large times.

Finite block effects are numerically analyzed.

Abstract

The non-equilibrium evolution of the block entanglement entropy is investigated in the XY chain in a transverse magnetic field after the Hamiltonian parameters are suddenly changed from and to arbitrary values. Using Toeplitz matrix representation and multidimensional phase methods, we provide analytic results for large blocks and for all times, showing explicitly the linear growth in time followed by saturation. The consequences of these analytic results are discussed and the effects of a finite block length is taken into account numerically.