Many-body localization phase transition

TLDR

The study uses exact diagonalization to investigate the many‑body localization transition in a random‑field spin‑1/2 chain. The authors analyze correlations in all high‑energy eigenstates of the spin‑1/2 chain via exact diagonalization, effectively probing the system at infinite temperature. They find that weak random fields yield thermal (ergodic) eigenstates, strong fields produce localized eigenstates with short‑range entanglement, and the transition exhibits finite‑size scaling suggestive of infinite‑randomness behavior with a diverging dynamic 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 $z\ensuremath{\rightarrow}\ensuremath{\infty}$.