Is there slow particle transport in the MBL phase?

TL;DR

This study investigates whether slow particle transport occurs in the many-body localized (MBL) phase by analyzing entanglement and number entropy distributions, concluding that slow entanglement growth is due to configurational entanglement, not particle transport.

Contribution

It provides evidence that slow entanglement growth in the MBL phase is not caused by particle transport but by configurational entanglement, based on entropy distribution analysis.

Findings

Saturation value of entanglement entropy is due to redistribution in probability distributions.

Number entropy distributions are system size converged with a sharp cut-off.

Results rule out slow particle transport deep in the MBL phase.

Abstract

We analyze the saturation value of the bipartite entanglement and number entropy starting from a random product state deep in the MBL phase. By studying the probability distributions of these entropies we find that the growth of the saturation value of the entanglement entropy stems from a significant reshuffling of the weight in the probability distributions from the bulk to the exponential tails. In contrast, the probability distributions of the saturation value of the number entropy are converged with system size, and exhibit a sharp cut-off for values of the number entropy which correspond to one particle fluctuating across the boundary between the two halves of the system. Our results therefore rule out slow particle transport deep in the MBL phase and confirm that the slow entanglement entropy production stems uniquely from configurational entanglement.