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Register a new userDual Fermion Approach to Susceptibility of Correlated Lattice Fermions
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In this paper, we show how the two-particle Green function (2PGF) can be obtained within the framework of the Dual Fermion approach. This facilitates the calculation of the susceptibility in strongly correlated systems where long-ranged non-local correlations cannot be neglected. We formulate the Bethe-Salpeter equations for the full vertex in the particle-particle and particle-hole channels and introduce an approximation for practical calculations. The scheme is applied to the two-dimensional Hubbard model at half filling. The spin-spin susceptibility is found to strongly increase for the wavevector $vc{q}=(pi,pi)$, indicating the antiferromagnetic instability. We find a suppression of the critical temperature compared to the mean-field result due to the incorporation of the non-local spin-fluctuations.
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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.
We present a purely diagrammatic derivation of the dual fermion scheme [Phys. Rev. B 77 (2008) 033101]. The derivation makes particularly clear that a similar scheme can be developed for an arbitrary reference system provided it has the same interaction term as the original system. Thereby no restrictions are imposed by the locality of the reference problem or by the nature of the original problem as a lattice one. We present new arguments in favour of keeping the dual denominator in the expression for the lattice self-energy independently of the truncation of the dual interaction. As an example we present the computational results for the half-filled 2D Hubbard model with the choice of a $2times2$ plaquette with periodic boundary conditions as a reference system. We observe that obtained results are in a good agreement with numerically exact lattice quantum Monte Carlo data.
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.
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.
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.
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