Non-equilibrium quantum relaxation across a localization-delocalization transition
arXiv:1407.7829 · doi:10.1103/PhysRevB.90.184202
Abstract
We consider the one-dimensional -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), , the excitations (fermions) are delocalized, but become localized for . We study the non-equilibrium relaxation of the system by applying two protocols: a sudden change of (quench dynamics) and a slow change of 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.
10 pages, 6 figures, published version
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