Thermalization, Dynamics and Many-Body Localization

Remarkably, a generic interacting system with many degrees of freedom is often well described by a random matrix drawn from an appropriate ensemble, which solely relies on the symmetries of the system. This is one of the central premises of quantum chaos theory which explains the fascinating universality of statistical properties of eigenvalues and eigenstates of generic systems. Such systems, slightly pushed out-of-equilibrium, are normally expected to relax diffusively. In this talk I will show that disordered and interacting systems which exhibit a many-body localization (MBL) transition, behave in a strikingly different manner than expected from the above tenets in both one dimensional [1,2] and two dimensional systems [3]. These systems thermalize subdiffusively, have a vanishing diffusion coefficient and cannot be described by usual random matrix ensembles [4]. I will show the implications of these results on thermalization in closed quantum systems, and will derive a general relation between statistical properties of matrix elements of physical observables and a dynamical property of the system [4]. I will finish my talk by presenting some promising future directions [5]. 

References:

[2] Bar Lev, Cohen and Reichman, Phys. Rev. Lett. 114, 100601 (2015).  

[3] Bar Lev and Reichman, EPL 113, 46001 (2016). 


[5] Luitz and Bar Lev, Ann. Phys. arXiv:1610.08993 (invited review, 2016).