Non-equilibrium quantum relaxation across a localization-delocalization transition
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 quasi-periodic 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.