Statistical mechanics is the framework that connects thermodynamics to the microscopic world. It hinges on the assumption of equilibration. Isolated quantum systems need not equilibrate; one example is given by the phenomenon known as many-body localization. The many-body localized phase constitutes the ultimate quantum glass. It transports neither heat nor charge; may possess orders disallowed in equilibrium by Peierls-Mermin-Wagner arguments; and, may exhibit coherent localized degrees of freedom even at high energy.
In this talk, I will briefly introduce the basic phenomena of many-body localization and review its theoretical and experimental status. I will then focus on the question of the existence of a finite energy density mobility edge. I will show that such a transition arises in the dynamics of a mean-field quantum glass model, the quantum random energy model, and then turn to the evidence for a similar transition in one dimensional spin chains.
References:
CRL, A. Pal, A. Scardicchio, PRL 113, 200405 (2014)
I. Mondragon-Shem, A. Pal, T. Hughes, CRL, arXiv:1501.03824
