  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.
