Anomalous Charge Transport Capacity in Models of Many-Body Localization

The complete understanding of Many-Body Localization (MBL) and its stability or potential breakdown at large system sizes remains unclear. In this work, we numerically investigate the \emph{charge transport capacity}---a quantity that upper-bounds the total amount of charge that can pass through a central cut in a one-dimensional lattice. For ergodic systems, including those following the Eigenstate Thermalization Hypothesis (ETH), the charge transport capacity scales linearly with the system size with slope $1/2$ (for spinless fermions or hard-core bosons at half-filling). In contrast, localized systems should have finite charge transport capacity in the thermodynamic limit. For a prototypical model of MBL, our calculations reveal that in the low-disorder regime, the disorder-averaged charge transport capacity grows linearly with system size, though with a slope smaller than that of fully ergodic systems. Surprisingly, in what is presumed to be very deep in the MBL regime, the disorder-averaged charge transport capacity remains small compared to $L$, yet increases with system size at an increasing rate for our system sizes, showing no saturation. This growth is driven by an increasing (with system size) integer number of particles capable of hopping across the central link when started in special initial states, reminiscent of but distinct from many-body resonances. Together, these results uncover a special type of many-body resonance relevant for understanding the possible breakdown of the MBL phase at finite sizes, and support that the simple $\ell$-bit model is insufficient to fully capture the dynamics of interacting localized systems. On the other hand, we also observe a finite Frobenius norm of the charge transport capacity operator at sufficiently strong disorder, which suggests that there exists some departure from ETH in this model in the thermodynamic limit, even if it falls short of strict MBL.