Entanglement entropy and thermalization in a hypercube model of many-body localization

Abstract: 
A schematic model of interacting spins in random field is introduced, which combines the symmetry of  hypercube with the simplicity of random regular graph with degree three. We study the many-body localization transition in this model. Namely, we investigate the transition in terms of the entanglement entropy and entanglement spectrum and stress the fundamental importance of finite-size corrections. We also show that the most significant indicator of the localization transition is the breakdown of eigenstate thermalization hypothesis.  At the transition, the distribution of matrix elements of local operators changes from Gasussian to bimodal. Such qualitative change also provides a good estimate for the critical disorder strength.