A research of nanosystems within the Hubbard model by mean field approximation

Background. The Hubbard model is widely used for description of strongly correlated electronic systems. Various approximate methods are used for investigation of these systems. The purpose of this paper is to investigate nanosystems within the Hubbard model by the method of motion equations for creation operators. Materials and methods. The mean field approximation allows to obtain a closed system of differential equations for finding creation operators. The Green's functions, correlation functions and an energy spectrum of nanosystem can be calculated using creation operators. Results. The developed approaches for finding the Green's functions within the Hubbard model by the mean field approximation were used to obtain the Green's functions of dimer, hexagon, pentagon and fullerene $С_{20}$. Conclusions. This work demonstrates that the energy spectrum of a nanosystem, obtained within the Hubbard model by the mean field approximation, is similar to the energy spectrum of this system, obtained within the Huckel model. This work also demonstrates that the Huckel model can be regarded as the Hubbard model within the mean field approximation.