Vestnik of the Mari State University

Димер в модели Хаббарда в приближении статических флуктуаций

Силантьев Анатолий Владимирович

Published Jan 1, 2012• 0 citations

Abstract

Anticommutator Green functions and the dimer energy spectrum in Hubbard model and the hydrogen molecule energy spectrum in Hubbard model are calculated in the approximation of statical fluctuations.

Related papers

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

G. I. Mironov

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.

The Physics of Metals and MetallographyDec 1, 20067 citations

Nanosystems in the static-fluctuation approximation Hubbard model

G. I. Mironov

The anticommutator Green’s functions, correlation functions, and ground-state energies of two-, three-, and four-atom nanosystems are calculated in the static-fluctuation approximation, and comparison with exact results is made.

Physics of the Solid StateJul 1, 20066 citations

Исследование наносистем в модели Хаббарда в приближении статических флуктуаций

Силантьев Анатолий Владимирович

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.

Известия высших учебных заведений. Поволжский регион. Физико-математические наукиJan 1, 20150 citations

Димер в модели Хаббарда

Силантьев Анатолий Владимирович

Background. Exactly solvable models are of great importance in quantum physics, as most models in quantum physics are not exactly solvable. The detailed analysis of exactly solvable model’s behavior can be made by exact solutions. The solutions of exactly solvable models, obtained by the approximation method, can be compared with exact solutions, used as standards. A dimer in the Hubbard model is an exactly solvable model. The purpose of this paper is to compare exact solutions obtained for a dimer in the Hubbard model, with solutions obtained for a dimer by approximation of static fluctuations. Materials and methods. In this study, to construct exact solutions and solutions in approximation of static fluctuations the authors used the method of motion equations for creation operators, the method of Green’s functions and the spectral theorem. The energy spectrum of a quantum system can be calculated by Green’s functions, as the poles of Green’s functions correspond to the energy spectrum of a quantum system. Knowing the Green’s functions, the spectral theorem allows to calculate the correlation functions of the quantum system. Results. Resulting from the usage of the methods of the quantum field theory there were obtained anticommutator Green’s functions for a dimer, that were both exact and in approximation of static fluctuations. Using the anticommutator Green’s functions the authors obtained correlation functions and the energy spectrum for a dimer. Conclusions. This work demonstrates that the energy spectrum of a dimer is split by a strong Coulomb repulsion of electrons on two Hubbard subbands and the “metal-insulator” transition occurs in a dimer. This work also demonstrates that several energy states of a dimer, obtained by the approximation of static fluctuations, coincide with energy states of a dimer, obtained by an exact solution.

Известия высших учебных заведений. Поволжский регион. Физико-математические наукиJan 1, 20150 citations

空間依存ホッピング下でのBose-Fermi Hubbard model の解析

Kenta Shiina

Mar 25, 20180 citations

Димер в расширенной модели Хаббарда

Анатолий Владимирович Силантьев

В рамках модели Хаббарда вычислены точно, а также в приближении статических флуктуаций антикоммутаторные функции Грина димера, его энергетический спектр и корреляционные функции. При расчете учитывалось взаимодействие электронов, находящихся на разных узлах. Показано, что такой учет приводит к расщеплению некоторых энергетических уровней и существенной перестройке энергетического спектра рассматриваемой системы.

Jan 1, 20140 citations