Abstract 2 December 2015

Ergodicity, entanglement, and many-body localization

Dmitry Abanin, Department of Theoretical Physics, University of Geneva

We are used to describing systems of many particles by statistical mechanics. However, recently it was realized that the basic postulate of statistical mechanics – ergodicity -- breaks down in so-called many-body localized systems, where disorder prevents particle transport and thermalization. In this talk, I will describe a recent theory of the many-body localized (MBL) phase, based on new insights from quantum entanglement. I will argue that, in contrast to ergodic systems, MBL eigenstates are not highly entangled, but rather obey so-called area law, typical of ground states in gapped systems. I will use this fact to show that MBL phase is characterized by an infinite number of emergent local conservation laws, in terms of which the Hamiltonian acquires a universal form. Turning to the experimental implications, I will show that MBL systems exhibit a universal response to quantum quenches: surprisingly, entanglement shows logarithmic in time growth, reminiscent of glasses, while local observables exhibit power-law approach to “equilibrium” values. I will close by discussing the transition between many-body localized and ergodic phases, as well as other recent developments in exploring ergodicty and its breaking in quantum many-body systems.

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