High-probability proof of many-body localization in one dimension

Extend the rigorous many-body localization result for one-dimensional spin chains from a set of disorder realizations having exponentially small probability to a result holding with high probability, under a suitable limited level attraction assumption controlling anomalously small level spacings.

Background

The paper describes a perturbative renormalization scheme that rigorously establishes many-body localization only on a resonance-free set of disorder realizations whose probability is bounded below by an exponentially small quantity in the system size. Although this result is mathematically useful and yields typical transport consequences through rare-region arguments, it does not establish localization for most disorder realizations.

The authors state that a high-probability result is strongly expected in one dimension at sufficiently strong disorder, provided a limited level attraction assumption is imposed. Proving such a result would require controlling many resonant regions simultaneously and showing that they cannot initiate unbounded thermal avalanches.