Dynamical obstruction to localization in a disordered spin chain

TL;DR

This paper investigates a disordered spin chain and finds a regime of slow, subdiffusive dynamics that challenges the traditional localization transition, suggesting a universal relaxation behavior instead.

Contribution

It introduces a new perspective on the transition between localized and ergodic phases, emphasizing the role of slow dynamics and spectral properties in disordered spin systems.

Findings

Identification of a maximal chaos region with enhanced susceptibility

Evidence of subdiffusive relaxation regime at moderate disorder

Spectral function inversely proportional to frequency indicating logarithmic relaxation

Abstract

We analyze a one-dimensional XXZ spin chain in a disordered magnetic field. As the main probes of the system's behavior we use the sensitivity of eigenstates to adiabatic transformations, as expressed through the fidelity susceptibility, in conjunction with the low frequency asymptotes of the spectral function. We identify a region of maximal chaos -- with exponentially enhanced susceptibility -- which separates the many-body localized phase from the diffusive ergodic phase. This regime is characterized by slow transport and we argue that the presence of such slow dynamics is incompatible with the localization transition in the thermodynamic limit. Instead of localizing, the system appears to enter a universal subdiffusive relaxation regime at moderate values of disorder, where the spectral function of the local longitudinal magnetization is inversely proportional to the frequency, corresponding to logarithmic in time relaxation of its auto-correlation function.