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We study the infinite temperature dynamics of a prototypical one-dimensionalsystem expected to exhibit many-body localization. Using numerically exactmethods, we establish the dynamical phase diagram of this system based on thestatistics of its eigenvalues and its dynamical behavior. We show that thenonergodic phase is reentrant as a function of the interaction strength,illustrating that localization can be reinforced by sufficiently stronginteractions even at infinite temperature. Surprisingly, within the accessibletime range, the ergodic phase shows subdiffusive behavior, suggesting that thediffusion coefficient vanishes throughout much of the phase diagram in thethermodynamic limit. Our findings strongly suggest that Wigner-Dyson statisticsof eigenvalue spacings may appear in a class of ergodic but subdiffusivesystems.

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