Many-body localized to ergodic transitions in a system with correlated disorder

We study the many-body localization (MBL) to ergodic phase transition in a simple model of correlated disorder in a spin chain, which can be tuned from an uncorrelated to an extremely correlated limit using a single parameter. Using several statistical measures, like gap-statistics and extremal entanglement spectrum distributions, we find the phase diagram in the the disorder-correlation plane. We show that one can use the average of sample variance of disorder as a single parameter which encodes the effects of the correlated disorder, and hence the distributions and averages of various statistics collapse into a single curve as a function of this parameter. This also allows us to analytically calculate the phase diagram in the disorder-correlation plane.