Nonequilibrium quantum relaxation across a localization-delocalization transition

Roósz, Gergő and Divakaran, U. and Rieger, H. and Iglói, Ferenc (2014) Nonequilibrium quantum relaxation across a localization-delocalization transition. PHYSICAL REVIEW B, 90 (18). ISSN 2469-9950

Preview

Text 1407.7829.pdf Available under License Creative Commons Attribution. Download (385kB) | Preview

Abstract

We consider the one-dimensional XX-model in a quasi-periodic transverse-field described by the Harper potential, which is equivalent to a tight-binding model of spinless fermions with a quasiperiodic chemical potential. For weak transverse field (chemical potential), h < hc, the excitations (fermions) are delocalized, but become localized for h > hc. We study the non-equilibrium relaxation of the system by applying two protocols: a sudden change of h (quench dynamics) and a slow change of h in time (adiabatic dynamics). For a quench into the delocalized (localized) phase, the entanglement entropy grows linearly (saturates) and the order parameter decreases exponentially (has a finite limiting value). For a critical quench the entropy increases algebraically with time, whereas the order parameter decreases with a stretched-exponential. The density of defects after an adiabatic field change through the critical point is shown to scale with a power of the rate of field change and a scaling relation for the exponent is derived.

Actions (login required)

Edit Item