We derive and study an effective spin model that explains the anomalous spin dynamics in the one-dimensional Hubbard model with strong potential disorder. Assuming that charges are localized, we show that spins are delocalized and their subdiffusive transport originates from a singular random distribution of spin exchange interactions. The exponent relevant for the subdiffusion is determined by the Anderson localization length and the density of the electrons. Although the analytical derivations are valid for low particle density, numerical results for the full model reveal a qualitative agreement up to half filling.

We develop a procedure which systematically generates all conserved operators in the disordered models of interacting fermions. Among these operators, we identify and count the independent and local integrals of motion (LIOM) which represent the hallmark of the many-body localization (MBL). The method is tested first on the prototype disordered chain of interacting spinless fermions. As expected for full MBL, we find for large enough disorder NM = 2 M − 1 independent and quasi-local LIOM with support on M consecutive sites. On the other hand, the study of the disordered Hubbard chain reveals that 3 M − 1 < NM 4 M /2 which is less than required for full MBL but much more than in the case of spinless fermions. arXiv:1708.08931v1 [cond-mat.str-el]

We study systems which are close to or within the many-body localized (MBL) regime and are driven by strong electric field. In the ergodic regime, the disorder extends applicability of the equilibrium linear-response theory to stronger drivings, whereas the response of the MBL systems is very distinctive, revealing currents with damped oscillations. The oscillation frequency is independent of driving and the damping is not due to heating but rather due to dephasing. The details of damping depend on the system's history reflecting nonergodicity of the MBL phase, while the frequency of the oscillations remains a robust hallmark of localization. We show that the distinctive characteristic of the driven MBL phase is also a logarithmic increase of the energy and the polarization with time.