THE IMPURITY ANDERSON MODEL REVISITED. A PROJECTOR OPERATOR SOLUTION. THE FINITE U CASE.

I. J. HAMAD; P. ROURA-BAS; E. V. ANDA

Buenos Aires

Conferencia; 27 International Conference on Low Temperature Physics.; 2014

Departamento de Física. Universidad Buenos Aires

A projector operator formalism is presented in order to describe the physics of the Anderson Impurity Hamiltonian. The treatment follows the line of previous works [Inagaki, Keiter] regarding theinfinite U case of this Hamiltonian. The method provides a very accurate calculation of the energy spectrum in the total spin S=0 sector and, in particular, the ground state energy in all theparameter space. The formalism requires the solution of three self-consistent integral equations. After solving them, the dependence of the ground state energy as a function of the impurityenergy is analyzed and the results compared with the corresponding ones obtained analytically for a non-interacting U=0 case, with excellent results. This is particularly significant because fromthe algebraic point of view the onebody and the many body problems are equivalent. The occupancy of the impurity is also studied for arbitrary U and compared with exact results obtained fromthe Bethe Ansatz [Tsvelik]. Finally, we include a magnetic field and study the magnetization and susceptibility of the impurity, from which we can extract the Kondo temperature. Thedependence of the Kondo scale with the parameters of the model is in very good agreement with well known results. This method can be extended to treat multy impurity systems.