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In this paper we present a method for obtaining the quasiband structure and the renormalized density of quasistates of strongly correlated systems with antiferromagnetic ordering. We calculate the electronic structure of La 2 CuO 4 in order to test this method. The first step required is to calculate the electronic structure from the local density approximation (LDA) in order to obtain the initial non-interacting ground state. The LDA density of states in strongly correlated systems usually presents serious discrepancies with experimental results. As is well known, these discrepancies, fundamentally concerning photoemission, are due to the fact that the dynamic correlation effects are not taken into account within the LDA. In order to include these effects, we obtain a self-energy potential which allows the initial LDA electronic structure to connect with that of the antiferromagnetic ground state arising from a Bogolyubov-like transformation. Within this new ground state, we determine an antiferromagnetic self-energy by means of a spin density wave procedure, and the interacting Green function yields a density of states which is in reasonable agreement with the experimental photoemission result.

With regard the Hubbard Hamiltonian, we use a Bogolyubov transformation and within a spin density wave mean field, where the antiferromagnetic correlations of wave vector Q =( π /a, π /a) are included. This gives a new energy spectrum that is calculated starting from the band structure of La2CuO4 determined in the local density formalism. We calculate the self-energy in this new ground state using the random phase approximation and a double Lorentzian as a non-interacting density of states. With this self-energy, Dyson's equation is solved by diagonalizing the Green's function in k-space. The density of states is obtained by considering the renormalization factor and the lifetimes of the quasiparticle states in each pole. This leads to the splitting of the input density of states that is calculated in the local density formalism.

A quasiparticle structure calculation for Sr 2 RuO 4 is performed. Starting from the band structure determined in the local density formalism, the Dyson's equation with self-energies arising from the Hubbard Hamiltonian, is solved by diagonalizing the Green's function in k -space. The density of states is obtained by considering the renormalization factor and the lifetimes of the quasiparticle states. We also obtain the Fermi surface without and with the inclusion of the strong correlations effects.

The non-copper layered perovskite, Sr 2 RuO 4 , is expected to be a very useful reference material for interpreting experiments on the high T c cuprate superconductors. A band structure calculation for Sr 2 RuO 4 is performed. Starting from the electronic structure determined in the local density formalism, the Dyson's equation with self-energies arising from the Hubbard hamiltonian is solved by diagonalizing the Green's function in k -space. The density of states is obtained by considering the renormalization factor and the life-times of the quasiparticle states in each pole of the interacting system. This leads to modification of the density of states calculated in the local density formalism, and the results fit experimental data not only in the position of peaks, but also in their intensity and in the number of states at Fermi level.

We are interested in the description of the Mott-Hubbard transition from a perturbation theory arising from a two-dimensional Hubbard model. We calculate the self-energy within the random phase approximation and a double-Lorentzian as a non-interacting density of states. The paramagnetic ground state is unstable for realistic values of U, since the self-energy presents some inconsistencies ; one of them is that its imaginary part presents more than one zero, which is a violation of the Luttinger theorem. We use a Bogolyubov transformation and within a spin density wave mean field, the antiferromagnetic correlations of wave vector Q = (π/a,π/a) are included. We recalculate the self-energy in the new ground state and then it is able to describe the Mott-Hubbard transition, and the Luttinger theorem is satisfied.

An approximated diagonalization of the Kondo lattice Hamiltonian is obtained considering an ansatz based on strongly correlated many body states which are combinations of charged fermionic excitations coupled to a kind of spin wave. For determined values of the density of states of the non-interacting system and Kondo Hamiltonian parameter, there is an interval of the J parameter in which a new and interesting ground state appears.