The many-body localization phase transition

TL;DR

This paper investigates the transition between localized and ergodic phases in a disordered quantum spin chain using exact diagonalization, revealing potential infinite-randomness criticality at the many-body localization transition.

Contribution

It provides numerical evidence for the nature of the many-body localization transition and suggests infinite-randomness scaling behavior at the critical point.

Findings

Eigenstates are thermal in the ergodic phase

Eigenstates are localized with short-range entanglement in the localized phase

The transition may exhibit infinite-randomness scaling with a diverging dynamic critical exponent

Abstract

We use exact diagonalization to explore the many-body localization transition in a random-field spin-1/2 chain. We examine the correlations within each many-body eigenstate, looking at all high-energy states and thus effectively working at infinite temperature. For weak random field the eigenstates are thermal, as expected in this nonlocalized, "ergodic" phase. For strong random field the eigenstates are localized, with only short-range entanglement. We roughly locate the localization transition and examine some of its finite-size scaling, finding that this quantum phase transition at nonzero temperature might be showing infinite-randomness scaling with a dynamic critical exponent $z\rightarrow\infty$.