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We investigate the static and dynamical behavior of 1D interacting fermionsin disordered Hubbard chains, contacted to semi-infinite leads. The chains aredescribed via the repulsive Anderson-Hubbard Hamiltonian, using static andtime-dependent lattice density-functional theory. The dynamical behavior of ourquantum transport system is performed via an integration scheme available inthe literature, which we modify via the recursive Lanczos method, to increaseits efficiency. To quantify the degree of localization due to disorder andinteractions, we adapt the definition of the inverse participation ratio toobtain an indicator which is both suitable for quantum transport geometries andwhich can be obtained within density-functional theory. Lattice densityfunctional theories are reviewed and, for contacted chains, we analyze themerits and limits of the coherent-potential approximation in describing thespectral properties, with interactions included via lattice density functionaltheory. Our approach appears to able to capture complex features due to thecompetition between disorder and interactions. Specifically, we find adynamical enhancement of delocalization in presence of a finite bias, and anincrease of the steady-state current induced by inter-particle interactions.This behavior is corroborated by results for the time-dependent densities andfor the inverse participation ratio. Using short isolated chains withinteraction and disorder, a brief comparative analysis between time-dependentdensity-functional theory and exact results is then given, followed by generalconclusive remarks.

Interacting fermions in 1D disordered lattices: Exploring localization and transport properties with lattice density-functional theories