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Area law in Imbrie's Many-Body Localization and its generalization

Mathematical Physics & Probability

Speaker: Evgeny Mozgunov, USC
Location: 2112 MSB
Start time: Wed, Apr 3 2019, 4:10PM

Many-body localization (MBL) is instrumental for recent theoretical work in condensed matter physics and quantum information. It allows to stabilize Floquet phases, explains the failure of adiabatic quantum optimization and has a potential to enhance quantum memory. Yet all of these results are not rigorous since MBL itself is not fully understood. We do not have rigorous results about its location in the phase diagram and its properties, with the exception of Imbrie's proof for a specific family of 1d spin chains, and the pioneering work of Basko, Aleiner, Altshuler for a specific 2d disordered electron system. Here we present the construction by Imbrie, prove an area law for it, and discuss a tentative definition of MBL that is consisted with that construction.