Statistics of entanglement spectrum across MBL to ergodic transition.

We show how the statistics of entanglement spectra change across the transition between a many body localized phase and an ergodic phase of an interacting disordered system. Using a disordered spin chain as a model, we numerically construct various measures and try to find an "order parameter" for the transition. The transition point obtained from this construction matches with those obtained from other indicators like the distribution of many-body energy gaps.