Long-range resonances in quasiperiodic many-body localization

TL;DR

This paper explores long-range resonances in quasiperiodic many-body localized systems, revealing atypical eigenstates with strong correlations and challenging traditional transition expectations.

Contribution

It uncovers a broad regime with fat-tailed correlation distributions and identifies quasi-degenerate resonant cat states in quasiperiodic MBL systems.

Findings

Discovery of fat-tailed distributions of correlations at strong quasiperiodic potential

Identification of long-range correlated eigenstates as resonant cat states

Challenging the expectation of a sharp ergodic-MBL transition in quasiperiodic systems

Abstract

We investigate long-range resonances in quasiperiodic many-body localized (MBL) systems. Focusing on the Heisenberg chain in a deterministic Aubry-Andr\'{e} potential, we complement standard diagnostics by analyzing the structure of long-distance pairwise correlations at high energy. Contrary to the expectation that the ergodic-MBL transition in quasiperiodic systems should be sharper due to the absence of Griffiths regions, we uncover a broad unconventional regime at strong quasiperiodic potential, characterized by fat-tailed distributions of longitudinal correlations at long distance. This reveals the presence of atypical eigenstates with strong long-range correlations in a regime where standard diagnostics indicate stable MBL. We further identify these anomalous eigenstates as quasi-degenerate pairs of resonant cat states, which exhibit entanglement at long distance. These findings advance the understanding of quasiperiodic MBL and identify density-correlation measurements in ultracold atomic systems as a probe of long-range resonances.