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We generalize the recently introduced dual fermion (DF) formalism for disordered fermion systems by including the effect of interactions. For an interacting disordered system the contributions to the full vertex function have to be separated into elastic and inelastic scattering processes, and addressed differently when constructing the DF diagrams. By applying our approach to the Anderson-Falicov-Kimball model and systematically restoring the nonlocal correlations in the DF lattice calculation, we show a significant improvement over the Dynamical Mean-Field Theory and the Coherent Potential Approximation for both one-particle and two-particle quantities.
While the coherent potential approximation (CPA) is the prevalent method for the study of disordered electronic systems, it fails to capture non-local correlations and Anderson localization. To incorporate such effects, we extend the dual fermion app
To reduce the rapidly growing computational cost of the dual fermion lattice calculation with increasing system size, we introduce two embedding schemes. One is the real fermion embedding, and the other is the dual fermion embedding. Our numerical te
Studying the strong correlation effects in interacting Dirac fermion systems is one of the most challenging problems in modern condensed matter physics. The long-range Coulomb interaction and the fermion-phonon interaction can lead to a variety of in
We apply the recently developed dual fermion algorithm for disordered interacting systems to the Anderson-Hubbard model. This algorithm is compared with dynamical cluster approximation calculations for a one-dimensional system to establish the qualit
We present a generalization of the recently developed dual fermion approach introduced for correlated lattices to non-equilibrium problems. In its local limit, the approach has been used to devise an efficient impurity solver, the superperturbation s