Dynamics of many-body localization

Following the field theoretic approach of Basko et al. [Ann. Phys. 321, 1126 (2006)], we study in detail the real-time dynamics of a system expected to exhibit many-body localization. In particular, for time scales inaccessible to exact methods, we demonstrate that within the second-Born approximation the temporal decay of the density-density correlation function is consistent with a finite value for t -> infinity, as expected in a nonergodic state. This behavior persists over a wide range of disorder and interaction strengths and suggests that the nonergodic phase is surprisingly robust compared to the prediction of Basko et al. We argue that this discrepancy may be resolved by the presence of a nonergodic, but metallic, phase.