Random cubic graph embedded in a hypercube: Entanglement spectrum and many-body localization

TL;DR

This paper introduces a spin model based on a random cubic graph embedded in a hypercube to study many-body localization, analyzing entanglement properties and the breakdown of thermalization.

Contribution

It presents a novel model combining hypercube symmetry with random cubic graph structure to investigate localization transitions and eigenstate thermalization failure.

Findings

Localization transition characterized by entanglement entropy changes

Eigenstate thermalization hypothesis fails at critical disorder strength

Distribution of matrix elements shifts from Gaussian to bimodal

Abstract

The schematic model of interacting spins is introduced, which combines the symmetry of hypercube with the simplicity of random regular graph with degree three, i.e. the random cubic graph. We study the localization transition in this model, which shares essential characteristics with the systems exhibiting many-body localization. Namely, we investigate the transition in terms of the entanglement entropy and entanglement spectrum. We also show that the most significant indicator of the localization transition is the failure of eigenstate thermalization hypothesis, when the distribution of matrix elements of local operators changes from Gasussian to bimodal. It also provides good estimate for the critical disorder strength.