On the density of states for the Hubbard model: pseudo-particle Keldysh diagram method – an alternative to DMFT?

It is shown how to construct Keldysh diagram technique for pseudo-particle approach to the Hubbard model. We propose self consistent equations for pseudo particle and electron Green functions in Keldysh diagram technique. Nonlocal effects (spatial dispersion) are included in single impurity problem in this method. Thus we can get rid of the artificial central peak (of Kondo type) in the density of states which is inevitable in Dynamical Mean Field Theory (DMFT). The changes in the density of states for 2D Hubbard model due to variation of Coulomb repulsion $U$ and electron concentration are analyzed.