Many-body localization and thermalization in the full probability distribution function of observables

• Published in: New journal of physics Vol. 14; no. 9; pp. 95020 - 95037
• Main Authors: Canovi, Elena, Rossini, Davide, Fazio, Rosario, Santoro, Giuseppe E, Silva, Alessandro
• Format: Journal Article
• Language: English
• Published: IOP Publishing 21.09.2012
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/14/9/095020

We investigate the relation between thermalization following a quantum quench and many-body localization in quasi-particle space in terms of the long-time full distribution function of physical observables. In particular, expanding on our recent work (Canovi et al 2011 Phys. Rev. B 83 094431), 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 qualitatively with the equilibrium ones, quantitative agreement is obtained only when integrability is fully broken and the relevant eigenstates are diffusive in quasi-particle space.