PIRSA:15030113

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

Grover, T. (2015). Universal Aspects of Many-body Localization Phase Transition and Eigenstate Thermalization. Perimeter Institute. https://pirsa.org/15030113

Grover, Tarun. Universal Aspects of Many-body Localization Phase Transition and Eigenstate Thermalization. Perimeter Institute, Mar. 10, 2015, https://pirsa.org/15030113 

          @misc{ pirsa_PIRSA:15030113,
            doi = {10.48660/15030113},
            url = {https://pirsa.org/15030113},
            author = {Grover, Tarun},
            keywords = {Condensed Matter},
            language = {en},
            title = {Universal Aspects of Many-body Localization Phase Transition and Eigenstate Thermalization},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {mar},
            note = {PIRSA:15030113 see, \url{https://pirsa.org}}
          }

Tarun Grover University of California, San Diego

DOI 10.48660/15030113
Collection
Talk Type Scientific Series
Subject

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.