Non-equilibrium quantum relaxation across a localization-delocalization transition

Gergö Roósz; Uma Divakaran; Heiko Rieger; Ferenc Iglói

doi:10.1103/physrevb.90.184202

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arXiv · 1407.7829

Non-equilibrium quantum relaxation across a localization-delocalization transition

Gergö Roósz·Uma Divakaran·Heiko Rieger·Ferenc Iglói

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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), $h h_c$. 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.

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Gergö Roósz, Uma Divakaran, Heiko Rieger, Ferenc Iglói. 2014-07-29. Non-equilibrium quantum relaxation across a localization-delocalization transition. https://doi.org/10.1103/physrevb.90.184202

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