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The Physics of Metals and Metallography

Calculation of Green’s functions for nanostructures in the Hubbard model in the approximation of static fluctuations

G. I. Mironov

Published Dec 1, 2006• 7 citations
Publisher

Abstract

Anticommutator Green’s functions, correlation functions, and magnetic moments (spins) for nanosystems consisting of 3, 4, and 5 atoms are calculated using the Hubbard model in the static-fluctuation approximation.
DOI
10.1134/s0031918x06120039

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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.
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 С20. 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.