Many-body localization in a fragmented Hilbert space

TL;DR

This paper investigates many-body localization in a model with fragmented Hilbert space, revealing how different Krylov subspaces exhibit signatures of MBL transition and varying scaling behaviors with system size.

Contribution

It demonstrates the existence of ergodic and localized Krylov subspaces in a fragmented Hilbert space, enabling analysis of MBL in larger systems than previously possible.

Findings

Certain Krylov subspaces show ergodic statistics and slow dimension growth.

Signatures of MBL transition are observed in level spacing and entanglement.

Critical disorder strength varies with system size depending on the subspace.

Abstract

We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than the full Hilbert space, but still exponentially. Such a property allows us to study the MBL phase transition in systems including more than $50$ spins. The different Krylov spaces that we consider show clear signatures of a many-body localization transition, both in the Kullback-Leibler divergence of the distribution of their level spacing ratio and their entanglement properties. But they also present distinct scalings with system size. Depending on the subspace, the critical disorder strength can be nearly independent of the system size or conversely show an approximately linear increase with the number of spins.