Research of nanosystems in the Hubbard model in approximation of static fluctuations

Background. The Hubbard model is widely used for theoretical description of strongly correlated electronic systems. Various approximate methods are used for investigation of these systems. At the present time there are four approaches to calculation of the Green's function in the approximation of static fluctuations. The purpose of this paper is to develop two more approaches to calculation of the Green's function in the approximation of static fluctuations. Materials and methods. The basis for the approximation of static fluctuations is the method of the motion equations for creation operators. The approximation of static fluctuations allows to obtain a closed system of differential equations for finding creation operators. The Green's functions, correlation functions and energy spectrum can be calculated using creation operators. Results. The developed approaches for finding the Green's functions in the Hubbard model by the approximation of static fluctuations were used to obtain the Green's functions of dimer, hexagon, pentagon and fullerene $С_{20}$. Conclusions. This work demonstrates that the Green's functions of dimer, hexagon, pentagon and fullerene $С_{20}$ obtained by the new approaches coincide with the Green's functions of these systems obtained by the earlier approaches.