Challenges to observation of many-body localization

TL;DR

This study investigates the long-time dynamics of disordered 1D Heisenberg spin chains to understand the challenges in experimentally observing many-body localization, highlighting persistent slow decay and differences with quasiperiodic potentials.

Contribution

It provides extensive numerical analysis showing the difficulty in definitively observing MBL due to slow dynamics and contrasts with quasiperiodic systems where localization signatures are more stable.

Findings

Imbalance decay persists beyond estimated critical disorder strengths.

No saturation of imbalance observed up to thousands of tunneling times.

Quasiperiodic potentials exhibit stable oscillation patterns indicating sustained localization.

Abstract

We study time dynamics of 1D disordered Heisenberg spin-1/2 chain focusing on a regime of large system sizes and a long time evolution. This regime is relevant for observation of many-body localization (MBL), a phenomenon that is expected to freeze the dynamics of the system and prevent it from reaching thermal equilibrium. Performing extensive numerical simulations of the imbalance, a quantity often employed in the experimental studies of MBL, we show that the regime of a slow power-law decay of imbalance persists to disorder strengths exceeding by at least a factor of 2 the current estimates of the critical disorder strength for MBL. Even though we investigate time evolution up to few thousands tunneling times, we observe no signs of the saturation of imbalance that would suggest freezing of system dynamics and provide a smoking gun evidence of MBL. We demonstrate that the situation is qualitatively different when the disorder is replaced by a quasiperiodic potential. In this case, we observe an emergence of a pattern of oscillations of the imbalance that is stable with respect to changes in the system size. This suggests that the dynamics of quasiperiodic systems remain fully local at the longest time scales we reach provided that the quasiperiodic potential is sufficiently strong. Our study identifies challenges in an unequivocal experimental observation of the phenomenon of MBL.