Non-equilibrium quantum relaxation across a localization-delocalization transition
Heiko Rieger
We consider the one-dimensional XX
model in a quasiperiodic 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 < h c
, the excitations (fermions) are delocalized, but
become localized for
h > h c . We study the nonequilibrium 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.
[1] G. Roósz, U. Divakaran, H. Rieger and F. Iglói Non-equilibrium quantum relaxation across a localization-delocalization transition |
Phys. Rev. B 90, 184202 (2014)
|
[pdf], [arXiv]
|
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