Many Body Localization Due to Correlated Disorder in Fock Space

The Hamiltonian of an interacting system of spinless fermions looks like that of a single particle hopping on a Fock graph in the presence of a random disordered potential. The coordination number of the Fock graph increases linearly with the system size L in 1D. Thus, in the thermodynamic limit, the disordered interacting problem in 1D maps on to an Anderson model with infinite coordination number. Despite this, this system displays localization which appears counterintuitive. The resolution lies in the on-site disorder on the Fock graph being highly corelated as they are derived from an exponentially smaller number of on-site disorder potentials in real space. Thus, such correlations have a strong effect on the localization properties of the corresponding many-body system. In this work we perform a systematic quantitative exploration of the nature of correlations of the Fock space potential required for localization. We show that changing the correlation strength can induce thermalization or localization in systems. We find that a linear variation of correlations with Hamming distance in Fock space is drives a thermal-MBL phase transition where the transition is driven by the correlation strength. Systems with the other forms of correlations we study are found to be ergodic.