Search

We investigate the static and dynamical behavior of 1D interacting fermions in disordered Hubbard chains, contacted to semi-infinite leads. The chains are described via the repulsive Anderson-Hubbard Hamiltonian, using static and time-dependent lattice density-functional theory. The dynamical behavior of our quantum transport system is performed via an integration scheme available in the literature, which we modify via the recursive Lanczos method, to increase its efficiency. To quantify the degree of localization due to disorder and interactions, we adapt the definition of the inverse participation ratio to obtain an indicator which is both suitable for quantum transport geometries and which can be obtained within density-functional theory. Lattice density functional theories are reviewed and, for contacted chains, we analyze the merits and limits of the coherent-potential approximation in describing the spectral properties, with interactions included via lattice density functional theory. Our approach appears to able to capture complex features due to the competition between disorder and interactions. Specifically, we find a dynamical enhancement of delocalization in presence of a finite bias, and an increase of the steady-state current induced by inter-particle interactions. This behavior is corroborated by results for the time-dependent densities and for the inverse participation ratio. Using short isolated chains with interaction and disorder, a brief comparative analysis between time-dependent density-functional theory and exact results is then given, followed by general conclusive remarks.

With the work performed in this research project, some fundamental aspects of TDDFT for strongly correlated systems have been characterized from several perspectives, such as the role of the exchange-correlation discontinuity in metal-insulator transitions and in quantum transport, the limitations but also the merits of adiabatic approximations, the necessity to include memory and nonlocal effects, to mention a few. Furthermore, TDDFT for strongly correlated lattice models has in fact turned into an active subfield of TDDFT, with new theoretical schemes, new theorems specifically proven for lattice (TD)DFT, applications to distant areas such as ultracold atoms and Kondo physics). Several possible directions can be easily envisaged to continue research in TDDFT: introducing memory and non local effects in the XC potentials (possibly exploiting more closely the connection with Kadanoff-Baym dynamics), magnetism in strongly correlated systems, electron-phonon interactions, etc. In particular, one important aspect, mentioned in the grant proposal and not significantly developed in the period covered by the grant, is the actual implementation of TDDFT within the ab-initio SeqQuest code. This aspect was only partially dealt with during the grant period (a large amount of preliminary work was done in this respect, but no concrete implementation is available and/or in close sight), and remains a priority in the future research plans of the principal investigator. To summarize, the research carried out during the grant period has provided a solid and attractive education profile to the PhD student Alexey Kartsev. It has also showed the great potential of TDDFT in describing the nonequilibrium dynamics of strongly correlated materials, and that there are many stimulating problems to be addressed in order to further develop an important approach such as TDDFT., AFRL-AFOSR-UK-TR-2012-0039. The original document contains color images.