a New Method to Study Disordered Systems with Interactions

Eric Dohner

Correlated, disordered lattice fermion systems out of equilibrium have been understudied, at least in part for lack of tools to study them. The development of a new method, the NE-DMFT+CPA, is explicated, for investigating the properties of these systems. This method combines DMFT and the CPA using the Kadanoff-Baym-Keldysh contour-time formalism to study the dynamics of interacting disordered systems out of equilibrium. The method is detailed, then applied to the case of the Anderson-Hubbard model: first to replicate well-known equilibrium results, then to study the case of the model under the effect of an interaction quench. Here the effect of disorder on the relaxation of the system is studied by the time-dependence of the energies and momentum distribution function, which display the screening of the Coulomb interaction by disorder. It is then used to examine the thermalization of the same system by using the fluctuation-dissipation theorem to extract the distribution function and thereby the effective temperature after relaxation. This allows the characterization of the effect of the interplay of the disorder strength and the Coulomb interaction on the thermalization behavior. It is found that the heating of the system due to the quench is mitigated by stronger disorder. Finally, current progress of the work to apply the method to binary alloy disorder and an interaction ramp is summarized. Binary disorder appears to have the effect of damping the initial transient of the potential energy more strongly than the comparable uniformly-disordered system. The relaxation of the energies under the effect of an interaction ramp suggests that the crossing of the kinetic energies may be affected by the form of the time-dependent interaction.

Ferenc Iglói, Heiko Rieger

A. MacKinnon

Georg Schwiete, K. B. Efetov

Considering disordered electron systems we suggest a scheme that allows us to include an electron-electron interaction into a supermatrix $\ensuremath{\sigma}$-model. The method is based on replacing the initial model of interacting electrons by a fully supersymmetric model. Although this replacement is not exact, it is a good approximation for a weak short range interaction and arbitrary disorder. The replacement makes the averaging over disorder and further manipulations straightforward and we come to a supermatrix $\ensuremath{\sigma}$-model containing an interaction term. The structure of the model is rather similar to the replica one, although the interaction term has a different form. We study the model making perturbation theory and renormalization group calculations. We check the renormalizability of the model in the first loop approximation and in the first order in the interaction. In this limit we reproduce the renormalization group equations known from earlier works. We hope that the new supermatrix $\ensuremath{\sigma}$-model may become a new tool for nonperturbative calculations for disordered systems with interaction.

Ilya A. Gruzberg

Jonathan M. Carter, A. MacKinnon

It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has suggested that interactions can substantially increase the localisation length in 1 dimensional systems and possibly lead to delocalisation in 2D. It has not been clear, however, to what extent these results are applicable to systems with a finite density of electrons. Among numerical approaches the transfer matrix method combined with finite size scaling has been particularly successful for non--interacting systems, whereas the density matrix renormalisation group successfully describes interacting systems. We have developed a new approach which combines elements of both these methods and have successfully applied it to spinless electrons with nearest neighbour interactions.