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

Entanglement Mean Field Theory and the Curie-Weiss Law

The mean field theory, in its different hues, form one of the most useful tools for calculating the single-body physical properties of a many-body system. It provides important information, like critical exponents, of the systems that do not yield to an exact analytical treatment. Here we propose an entanglement mean field theory (EMFT) to obtain the behavior of the two-body physical properties of such systems. We apply this theory to predict the phases in paradigmatic strongly correlated systems, viz. the transverse anisotropic XY, the transverse XX, and the Heisenberg models. We find the critical exponents of different physical quantities in the EMFT limit, and in the case of the Heisenberg model, we obtain the Curie-Weiss law for correlations. While the exemplary models have all been chosen to be quantum ones, classical many-body models also render themselves to such a treatment, at the level of correlations.Comment: 5 pages, 4 figure