# Many body localization, thermalization, and the localization transition: insights from the entanglement spectrum

**Speaker:**Rahul Nandkishore

**When:**April 28, 2017 (Fri), 12:00PM to 01:00PM (add to my calendar)

**Location:**SCI 352

*This event is part of the Biophysics/Condensed Matter Seminar Series. *

I discuss universal structure in the pattern of entanglement of many body localized (MBL) and thermalizing phases. There is far more universal structure than is captured by the entanglement entropy - and some if it can be extracted from the entanglement spectrum using diagnostics inspired by random matrix theory. Examining the thermalizing phase through this lens, we discover new universal structure consistent with but going beyond that predicted by eigenstate thermalization (ETH). In the MBL phase, we discover universal structure in the high energy part of the entanglement spectrum indicative of a residual `memory of criticality,’ which persists in the wave functions arbitrarily deep into the localized phase. Armed with this insight, we attack the many body localization transition by working deep within the localized phase, where finite size effects are well under control. A consideration of appropriate diagnostics based on the entanglement spectrum allows us to identify the MBL-quantum critical crossover for the first time in exact numerics. This allows us to place an upper bound on the critical disorder strength for localization, to complement the lower bounds that have previously been obtained.