Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice

TL;DR

This study investigates the dynamics of a one-dimensional disordered fermionic system at infinite temperature, revealing a reentrant many-body localized phase and subdiffusive behavior in the ergodic phase, challenging traditional diffusion assumptions.

Contribution

It demonstrates that strong interactions can reinforce localization and shows the emergence of subdiffusive dynamics in ergodic phases, supported by numerical analysis of eigenvalue statistics.

Findings

Reentrant nonergodic phase as a function of interaction strength

Subdiffusive behavior observed in the ergodic phase

Eigenvalue statistics consistent with Wigner-Dyson in ergodic regime

Abstract

We study the infinite temperature dynamics of a prototypical one-dimensional system expected to exhibit many-body localization. Using numerically exact methods, we establish the dynamical phase diagram of this system based on the statistics of its eigenvalues and its dynamical behavior. We show that the nonergodic phase is reentrant as a function of the interaction strength, illustrating that localization can be reinforced by sufficiently strong interactions even at infinite temperature. Surprisingly, within the accessible time range, the ergodic phase shows subdiffusive behavior, suggesting that the diffusion coefficient vanishes throughout much of the phase diagram in the thermodynamic limit. Our findings strongly suggest that Wigner-Dyson statistics of eigenvalue spacings may appear in a class of ergodic but subdiffusive systems.