The Impurity Anderson Hamiltonian Revisited. An Exact Projector Operator Solution.

VICTOR LOPES DA SILVA; P. ROURA-BAS; I. J. HAMAD; E. V. ANDA

Aguas de Lindoia, San Pablo.

Congreso; XXXVI Encontro Nacional de Materia Condensada; 2013

Sociedade Brasileira de Física

The Impurity Anderson Hamiltonian has received large attention in the last 50 years, since the pioneering work of J. Kondo who explained the behavior of the resistivity as a function of temperature of metals doped with 3d transition metal or 4f rare earth impurities. This Hamiltonian has been on the base of the heavy fermion physics. As the Hubbard Hamiltonian in infinite dimension can be transformed into a self-consistent renormalized one impurity Anderson Hamiltonian, within the Dynamical Mean Field Theory (DMFT) (1), this model has permitted as well the study of several aspects of many body physics as for instance the metal non-metal transition taking place in various systems. More recently the Kondo effect have received a great attention associated to the many body properties of highly correlated electronic nanosystem, as quantum dots or structures of quantum dots. The Hamiltonian has been solved by a variety of different numerical approaches as it is the case of LDECA (2), NRG (3) and DMRG (4) or more algebraic methods as the Slave Bosons and the Non-crossing (NCA) (5) or One-crossing (OCA) (6) approximations. Although the two first mentioned numerical ones can be considered to be exact, while the other ones are only approximations with different capabilities of catching the physics involved, they as well have several limitations regarding the complexity of the system and the temperature. Moreover the dynamical properties are not completely well characterized, particularly within the NRG approximation. Here we propose an algebraic method to solve the Anderson Hamiltonian which consists in projecting the total Hilbert space into a subspace where the electrons are filling the Fermi sea up to the Fermi level. To operate in this subspace the Hamiltonian has to be renormalized. A systematic and self-consistent renormalization of the Hamiltonian permits to obtain the ground state properties, the Kondo temperature and the magnetic susceptibility as a function of the parameters of the system. As formally the many body interactions do not introduce any additional complexity in comparison to the one body problem, we were able to prove the exactness of our calculations comparing our results with the well-known results of the one body system.