MRSej, Vol. 6, No.1, pp.141-153, 2004

**THE ****INVESTIGATION ****OF ****THE ***B - **U - **V ***HUBBARD ****MODEL
**

G.I. Mironov.

*Mari **State ** Pedagogical Institute, 424002 Ioshkar-Ola *

We investigate the *B-U-V * Hubbard model in the Static-Fluctuation Approximation. The first part of the article is devoted to the exact solution of the Hubbard model in the case of two sites of the crystal lattice. We got and solved system of 24 differential equations for the 24 Fermi operators. The anticommutator Green's function for dimer was derived. In the second part we calculate the anticommutator Green's function for dimer in the Static-Fluctuation Approximation. Comparison of the exact and approximate solutions shows that the Static-Fluctuation Approximation adequately describes the Hubbard model for case of two sites of the crystal lattice. The third part is concerned with the solution in the Static-Fluctuation Approximation of the two-dimensional Hubbard model. We investigate the energy spectrum of the two-dimensional Hubbard model, the numerator of the anticommutator Green's function. It should be noted that in the case of strong correlations, the ground-state energy of the antiferromagnetic phase is found to be lower than that of the paramagnetic phase.

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