On Stark Many-body localization perturbed by harmonic potential

Ruixiao Yao, Titas Chanda, Jakub Zakrzewski

Published 2021-03-22Version 1

We discuss properties of interacting spinless fermions in a tilted optical lattice as modeled by Heisenberg spin chain in magnetic (or electric) field changing linearly across the chain. The system shows genuine features of strong localization for a sufficiently large tilt with distinct features different from disorder induced localization. In particular, Stark many-body localization is characterized in time dynamics by a linear increase of the entanglement entropy followed by a saturation at a constant, time independent value -- both the number (classical) and the configuration (quantum) entropies saturate to a constant value. Similarly, the correlation with the initial state (the so called imbalance) stabilizes at a constant value (modulo large fluctuations coming from short time Bloch-type oscillations). The presence of an additional harmonic potential profoundly affects the dynamics of the model -- its behavior resembles standard MBL characteristics -- the logarithmic growth of the entanglement entropy in particular. In that case, we find strong revival phenomena associated with the manifold of equally spaced states, degenerate in the absence of the harmonic potential.