One-loop approximation for the Hubbard model

The diagram technique for the one-band Hubbard model is formulated for the case of moderate to strong Hubbard repulsion. The expansion in powers of the hopping constant is expressed in terms of site cumulants of electron creation and annihilation operators. For the Green's function, an equation of the Larkin type is derived and solved in a one-loop approximation for the case of two dimensions, nearest-neighbor hopping, and half-filling. The obtained four-band structure of the spectrum and the shapes of the spectral function are close to those observed in Monte Carlo calculations. The four-band structure has its origin in the regions of large damping which separate the bands. It is shown that the maxima forming the bands are of a dissimilar origin in different regions of the Brillouin zone.