Método atômico para o modelo de Anderson em presença de um campo magnético externo. - Becerra, Víctor Leonardo Fernández (2011)
We develop the atomic method (AM) for the Anderson impurity model under an external magnetic field. The Green s functions (GF) representing the exact solution of the impurity problem is written in terms of an effective cumulant, that in the atomic method is replaced by the atomic cumulant obtained from the atomic Green function. In the atomic model the conduction band is collapsed into two localized levels, everyone depending on spin xq s and related to the spin up and down channels. Therefore, the problem is parametrized by xq"(#), and every spin channel need to be found self consistently in a way that a generalized Friedel sum rule, that takes into account the magnetic field ~B, must be satisfied. The calculation of the parameters mentioned above allow us to obtain the approximate GF of the impurity Anderson model, and the spectral densities depending on the magnetic field ~B. From these results, we calculate the Kondo splitting and compare it with similar results obtained previously within the numerical renormalization group method. We also obtain results within the atomic method for the phase shift and agnetization as a function of the magnetic field. These results were compared with those obtained by means of the Bethe ansatz (BA) for the Kondo model. In the Kondo regime the agreement between the BA and the AM is good, however in the boundary between the Kondo and the mixed valence regime the results differ because the charge fluctuations in the Anderson model become important. As an application in transport theory, we calculate the conductance of a quantum dot immersed into a ballistic channel and we generalize the method to the periodic case.