Properties of the half-filled Hubbard model investigated by the strong coupling diagram technique

The equation for the electron Green's function of the fermionic Hubbard model, derived using the strong coupling diagram technique, is solved self-consistently for the near-neighbor form of the kinetic energy and for half-filling. In this case the Mott transition occurs at the Hubbard repulsion $U_c\approx 6.96t$, where $t$ is the hopping constant. The calculated spectral functions, density of states and momentum distribution are compared with results of Monte Carlo simulations. A satisfactory agreement was found for $U>U_c$ and for temperatures, at which magnetic ordering and spin correlations are suppressed. For $U<U_c$ and lower temperatures the theory describes qualitatively correctly positions and widths of spectral continua, variations of spectral shapes and occupation numbers with changing wave vector and repulsion. The locations of spectral maxima turn out to be close to the positions of $\delta$-function peaks in the Hubbard-I approximation.