Universal Aspects of Many-body Localization Phase Transition and Eigenstate Thermalization

Abstract

Does a generic quantum system necessarily thermalize? Recent developments in disordered many-body quantum systems have provided crucial insights into this long-standing question. It has been found that sufficiently disordered systems may fail to thermalize leading to a 'many-body localized' phase. In this phase, the fundamental assumption underlying equilibrium statistical mechanics, namely, the equal likelihood for all states at the same energy, breaks down. A fundamental question is: what happens as the disorder becomes weaker so that one approaches the localization-delocalization transition? For example, does the system thermalize *at* the transition? 

In this talk, I will show that very general considerations on the scaling of entanglement entropy close to the transition imply that at a continuous many-body localization transition, the system is necessarily ergodic.

Finally, I will present recent results on "eigenstate thermalization", a long standing hypothesis which posits that a single eigenstate hides within itself a thermal ensemble. In particular, I will discuss which class of operators do or do not satisfy eigenstate thermalization.