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Many-body localisation in interacting quantum systems can be cast as adisordered hopping problem on the underlying Fock-space graph. A crucialfeature of the effective Fock-space disorder is that the Fock-space siteenergies are strongly correlated -- maximally so for sites separated by afinite distance on the graph. Motivated by this, and to understand the effectof such correlations more fundamentally, we study Anderson localisation onCayley trees and random regular graphs, with maximally correlated disorder.Since such correlations suppress short distance fluctuations in the disorderpotential, one might naively suppose they disfavour localisation. We findhowever that there exists an Anderson transition, and indeed that localisationis more robust in the sense that the critical disorder scales with graphconnectivity $K$ as $\sqrt{K}$, in marked contrast to $K\ln K$ in theuncorrelated case. This scaling is argued to be intimately connected to thestability of many-body localisation. Our analysis centres on an exact recursiveformulation for the local propagators as well as a self-consistent mean-fieldtheory; with results corroborated using exact diagonalisation.

Localisation on certain graphs with strongly correlated disorder