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Register a new userDual-fermion approach to interacting disordered fermion systems
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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.
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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 approach to disordered non-interacting systems using the replica method. Results for single- and two- particle quantities show good agreement with cluster extensions of the CPA; moreover, weak localization is captured. As a natural extension of the CPA, our method presents an alternative to the existing cluster theories. It can be used in various applications, including the study of disordered interacting systems, or for the description of non-local effects in electronic structure calculations.
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 tests show that the real fermion and dual fermion embedding approaches converge to essentially the same result. The application on the Anderson disorder and Hubbard models shows that these embedding algorithms converge more quickly with system size as compared to the conventional dual fermion method, for the calculation of both single-particle and two-particle quantities.
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 intriguing properties. In the strong-coupling regime, weak-coupling perturbation theory breaks down. The validity of $1/N$ expansion with $N$ being the fermion flavor is also in doubt since $N$ equals to $2$ or $4$ in realistic systems. Here, we investigate the interaction between (1+2)- and (1+3)-dimensional massless Dirac fermions and a generic scalar boson, and develop an efficient non-perturbative approach to access the strong-coupling regime. We first derive a number of self-consistently coupled Ward-Takahashi identities based on a careful symmetry analysis and then use these identities to show that the full fermion-boson vertex function is solely determined by the full fermion propagator. Making use of this result, we rigorously prove that the full fermion propagator satisfies an exact and self-closed Dyson-Schwinger integral equation, which can be solved by employing numerical methods. A major advantage of our non-perturbative approach is that there is no need to employ any small expansion parameter. Our approach provides a unified theoretical framework for studying strong Coulomb and fermion-phonon interactions. It may also be used to approximately handle the Yukawa coupling between fermions and order-parameter fluctuations around continuous quantum critical points. Our approach is applied to treat the Coulomb interaction in undoped graphene. We find that the renormalized fermion velocity exhibits a logarithmic momentum-dependence but is nearly energy independent, and that no excitonic gap is generated by the Coulomb interaction. These theoretical results are consistent with experiments in graphene.
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 quality of the approximation in comparison with an established cluster method. We continue with a three-dimensional (3d) system and look at the antiferromagnetic, Mott and Anderson localization transitions. The dual fermion approach leads to quantitative as well as qualitative improvement of the dynamical mean-field results and it allows one to calculate the hysteresis in the double occupancy in 3d taking into account nonlocal correlations.
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 solver for the Anderson impurity model (AIM). Here we show that the general dual perturbation theory can be formulated on the Keldysh contour. Starting from a reference Hamiltonian system, in which the time-dependent solution is found by exact diagonalization, we make a dual perturbation expansion in order to account for the relaxation effects from the fermionic bath. Simple test results for closed as well as open quantum systems in a fermionic bath are presented.
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