Quantum relaxation and finite-size effects in the XY chain in a transverse field after global quenches

¹ Theoretische Physik, Universität des Saarlandes - 66041 Saarbrücken, Germany, EU
² Wigner Research Centre, Institute for Solid State Physics and Optics H-1525 Budapest, P.O. Box 49, Hungary, EU
³ Institute of Theoretical Physics, Szeged University - H-6720 Szeged, Hungary, EU

^(a) bebla@lusi.uni-sb.de
^(b) h.rieger@mx.uni-saarland.de
^(c) igloi.ferenc@wigner.mta.hu

Received: 15 May 2012
Accepted: 12 July 2012

Abstract

We consider global quenches in the quantum XY chain in a transverse field and study the nonequilibrium relaxation of the magnetization and the correlation function as well as the entanglement entropy in finite systems. For quenches in the ordered phase the exact results are well described by a semiclassical theory (SCT) in terms of ballistically moving quasi-particle pairs. For finite systems quasi-periodic behaviour of the dynamical evolution of the local order parameter and the correlation functions is predicted correctly including the period length, an exponential relaxation, a quasi-stationary regime and an exponential recurrence in one period. In the thermodynamic limit the SCT is exact for the entanglement entropy and its modified version following the method of Calabrese P. et al., J. Stat. Mech. (2012) P07016, is exact for the magnetization and the correlation function, too. The stationary correlation function is shown to be described by a generalized Gibbs ensemble.