Absence of Diffusion in an Interacting System of Spinless Fermions on a One-Dimensional Disordered Lattice

TLDR

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 find that the nonergodic phase reenters with increasing interaction strength, indicating that strong interactions can reinforce localization even at infinite temperature, while the ergodic phase exhibits subdiffusive dynamics with a vanishing diffusion coefficient, suggesting that Wigner‑Dyson eigenvalue statistics may arise in ergodic but subdiffusive systems.

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.