On the structure of typical states of a disordered Richardson model and many-body localization

TL;DR

This paper investigates the structure of typical states in a disordered Richardson model, revealing relationships between localization measures and delocalization behavior, with implications for many-body localization and spin glass dynamics.

Contribution

It introduces a detailed numerical analysis of the Richardson model, establishing a simple relation between localization metrics and exploring the delocalized phase in the thermodynamic limit.

Findings

Relation between inverse participation ratio and Edwards-Anderson parameter

Delocalized phase extends over all coupling strengths in the thermodynamic limit

Similarity between eigenstate spread and hopping on percolated hypercube

Abstract

We present a thorough numerical study of the Richardson model with quenched disorder (a fully-connected XX-model with longitudinal random fields). We study the onset of delocalization in typical states (many-body delocalization) and the delocalized phase which extends over the whole range of coupling strength in the thermodynamic limit. We find a relation between the inverse participation ratio, the Edwards-Anderson order parameter and the average Hamming distance between spin configurations covered by a typical eigenstate for which we conjecture a remarkably simple form for the thermodynamic limit. We also studied the random process defined by the spread of a typical eigenstate on configuration space, highlighting several similarities with hopping on percolated hypercube, a process used to mimic the slow relaxation of spin glasses.