Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase

The self-averaging behavior of interacting many-body quantum systems has been mostly studied at equilibrium. The present paper addresses what happens out of equilibrium, as the increase of the strength of on-site disorder takes the system to the localized phase. We consider two local and two nonlocal quantities of great experimental and theoretical interest. In the delocalized phase, self-averaging depends on the observable and on the timescale, but the picture simplifies substantially when localization is reached. In the localized phase, the local observables become self-averaging at all times while the nonlocal quantities are throughout non-self-averaging. These behaviors are explained and scaling analysis is provided using the ℓ-bit model and a toy model.
E.J.T.-H. acknowledges funding from VIEP-BUAP (Grant Nos. MEBJ-EXC19-G, LUAGEXC19-G), Mexico. He is also grateful to LNS-BUAP for allowing use of their supercomputing facility. M.S. and L.F.S. were supported by the NSF Grant No. DMR-1603418 and gratefully acknowledges support from the Simons Center for Geometry and Physics, Stony Brook University at which some of the research for this paper was performed. F.P.B. thanks the Consejer´ıa de Conocimiento, Investigaci´on y Universidad, Junta de Andaluc´ıa and European Regional Development Fund (ERDF), ref. SOMM17/6105/UGR. Additional computer resources supporting this work were provided by the Universidad de Huelva CEAFMC High Performance Computer located in the Campus Universitario el Carmen and funded by FEDER/MINECO project UNHU15CE-2848. L.F.S. is supported by the NSF Grant No. DMR-1936006. Part of this work was performed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. G.D.T. acknowledges the hospitality of MPIPKS Dresden, where part of the work was performed.