Low Temperature Physics

Approximation of static fluctuations for Hubbard’s model

V. V. Loskutov, G. I. Mironov, Raoul Rashidovich Nigmatullin

Published Mar 1, 1996• 15 citations

Abstract

The application of statistical fluctuation method to Hubbard’s model is demonstrated. Expressions for anticommutator Green’s function, magnetization, and concentration are derived. The results are compared with the exact solution in the atomic limit and the exact solution in one-dimensional model for T=0.

DOI: 10.1063/10.0033957

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

Investigation of the single-particle Green’s function in a bipartite Hubbard model in the static-fluctuations approximation

G. I. Mironov

The single-particle anticommutator Green’s function of a two-sublattice two-dimensional Hubbard model is calculated in the static-fluctuations approximation taking account of electron transfer to the nearest and second-nearest neighboring sites of the crystal lattice. The behavior of the bipartite Hubbard model for strong and weak coupling is investigated.

Low Temperature PhysicsDec 1, 20052 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

The ground-state energy of the B-B′-U Hubbard model in the static-fluctuation approximation

G. I. Mironov

The ground-state energy of the two-sublattice two-dimensional Hubbard model is calculated in the static-fluctuation approximation with allowance for electron transfer from sites to next-to-nearest neighbor sites. In a specific case, the energy of the one-dimensional Hubbard model is calculated and compared with an exact solution.

Physics of the Solid StateFeb 1, 20028 citations

The atomic method for the Hubbard dimer

Renan Lira Nunes, Marcos Sergio Figueira da Silva

The single-band Hubbard Hamiltonian [1] is the simplest model of interacting electrons in a lattice.It was developed by John Hubbard, who introduced the model to take into account the local electronic correlations in narrow energy bands.The model has a kinetic term that allows hopping of electrons between atomic sites and a term that considers the on-site interaction between electrons.This model is largely used in solid state physics to study magnetic properties of solids, insulator-metal transition (Mott transition) and high temperature superconductors.However, this is a problem that has exact analytical solution in a very few limiting cases and must be treated approximately or numerically.In this work, we propose a new methodology to analytically solve the Hubbard Hamiltonian, mapping it into a two-site model (the Hubbard dimer).To obtain the Green's function for the lattice, we employed the cumulant expansion technique, using as a 'seed' the exact two-site Green's function (the atomic method) [2].From the Green's function, we obtained the density of states [DOS] and the occupation numbers as functions of the external parameters of the model, and compared the results with the Hubbard I approximation [1].

Brazilian Workshop on Semiconductor PhysicsAug 19, 20171 citation