MBL-Ergodic Transitions in Systems with Correlated Disorder*

We study transitions from many body localized to ergodic phase in one dimensional spin systems with correlated disorder. Using two different parameters to tune the width and correlations of the random couplings separately, we derive a phase diagram in the width-correlation plane. We understand the phase diagram in terms of an effective single parameter related to the sample variance of the couplings. This allows us to track the phase boundary analytically in this model.