Challenges to observation of many-body localization

We study time dynamics of 1D disordered Heisenberg spin-1/2 chains 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 the few thousands of tunneling times, we observe no signs of the saturation of imbalance that would suggest freezing of system dynamics and provide 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 remains fully local at the longest timescales we reach, provided that the quasiperiodic potential is sufficiently strong. Our study identifies challenges in an unequivocal experimental observation of the phenomenon of MBL.

Automated summary

This study investigates the time dynamics of 1D disordered Heisenberg spin-1/2 chains and finds that the regime of slow power-law decay of imbalance persists even at disorder strengths exceeding the critical disorder strength for many-body localization (MBL). However, when the disorder is replaced by a quasiperiodic potential, an emergence of a stable pattern of imbalance oscillations is observed. The study highlights the challenges in experimentally observing MBL phenomenon.