3 research outputs found
Many-body localization and thermalization in the full probability distribution function of observables
We investigate the relation between thermalization following a quantum quench
and many-body localization in quasiparticle space in terms of the long-time
full distribution function of physical observables. In particular, expanding on
our recent work [E. Canovi {\em et al.}, Phys. Rev. B {\bf 83}, 094431 (2011)],
we focus on the long-time behavior of an integrable XXZ chain subject to an
integrability-breaking perturbation. After a characterization of the breaking
of integrability and the associated localization/delocalization transition
using the level spacing statistics and the properties of the eigenstates, we
study the effect of integrability-breaking on the asymptotic state after a
quantum quench of the anisotropy parameter, looking at the behavior of the full
probability distribution of the transverse and longitudinal magnetization of a
subsystem. We compare the resulting distributions with those obtained in
equilibrium at an effective temperature set by the initial energy. We find
that, while the long time distribution functions appear to always agree {\it
qualitatively} with the equilibrium ones, {\it quantitative} agreement is
obtained only when integrability is fully broken and the relevant eigenstates
are diffusive in quasi-particle space.Comment: 18 pages, 11 figure
Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
We consider the time evolution of order parameter correlation functions after
a sudden quantum quench of the magnetic field in the transverse field Ising
chain. Using two novel methods based on determinants and form factor sums
respectively, we derive analytic expressions for the asymptotic behaviour of
one and two point correlators. We discuss quenches within the ordered and
disordered phases as well as quenches between the phases and to the quantum
critical point. We give detailed account of both methods.Comment: 65 pages, 21 figures, some typos correcte