Anderson Localization on Husimi Trees and its implications for Many-Body localization

TL;DR

This paper investigates how local loops in Husimi trees influence Anderson localization, revealing that loops enhance resonances and hybridization, thus affecting localization properties relevant to many-body localization.

Contribution

It provides an exact solution demonstrating the impact of local loops on localization, bridging the gap between single-particle Anderson models and many-body localization phenomenology.

Findings

Local loops increase resonant processes, lowering the critical disorder.

Loops promote local hybridization, enlarging localized eigenstates.

Results reconcile differences between MBL phenomenology and Anderson models.

Abstract

Motivated by the analogy between many-body localization (MBL) and single-particle Anderson localization on hierarchical graphs, we study localization on the Husimi tree, a generalization of the Bethe lattice with a finite density of local loops of arbitrary but finite length. The exact solution of the model provides a transparent and quantitative framework to systematically inspect the effect of loops on localization. Our analysis indicates that local loops enhance resonant processes, thereby reducing the critical disorder with increasing their number and size. At the same time, loops promote local hybridization, leading to an increase in the spatial extent of localized eigenstates. These effects reconcile key discrepancies between MBL phenomenology and its single-particle Anderson analog. These results show that local loops are a crucial structural ingredient for realistic single-particle analogies to many-body Hilbert spaces.