The atomic approach to the Anderson model for the finite U case: application to a quantum dot

In the present work we apply the atomic approach to the single-impurity Anderson model (SIAM). A general formulation of this approach, that can be applied both to the impurity and to the lattice Anderson Hamiltonian, was developed in a previous work (Foglio et al 2009 arxiv: 0903.0139v2 [cond-mat.str-el]). The method starts from the cumulant expansion of the periodic Anderson model, employing the hybridization as a perturbation. The atomic Anderson limit is analytically solved and its sixteen eigenenergies and eigenstates are obtained. This atomic Anderson solution, which we call the AAS, has all the fundamental excitations that generate the Kondo effect, and in the atomic approach is employed as a 'seed' to generate the approximate solutions for finite U. The width of the conduction band is reduced to zero in the AAS, and we choose its position such that the Friedel sum rule is satisfied, close to the chemical potential mu. We perform a complete study of the density of states of the SIAM over the whole relevant range of parameters: the empty dot, intermediate valence, Kondo and magnetic regimes. In the Kondo regime we obtain a density of states that characterizes well the structure of the Kondo peak. To show the usefulness of the method we have calculated the conductance of a quantum dot, side-coupled to a conduction band.