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PRSM

Self Consistent RPA applied to the extended Hubbard Model

Said Harir, Mohamed Bennai, Y. Boughaleb, M. Fliyou

Published Mar 17, 2011• 0 citations
Publisher

Abstract

Using the extended Hubbard model with the Self Consistent Random Phase Approximation (SCRPA), we study the intersite interaction effect on the dynamics of N electrons. We consider the extended Hubbard model containing intrasite and intersite interactions, and we apply this model to a system of two interacting atoms, where each atom presents one free electron. The resolution of this tow sites problem is done by the SCRPA approximation; our calculations allow as studying the intersite interaction effect on the excitation energies of system. We have showed that the attractive interaction between the electrons of the neighbour’s atoms is the origin of supplementary conductivity of the system.

DOI
10.34874/prsm.mjcm-vol8iss0.187

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Using the extended Hubbard model with the Self Consistent Random Phase Approximation (SCRPA), we study the intersite interaction effect on the dynamics of N electrons. We consider the extended Hubbard model containing intrasite and intersite interactions, and we apply this model to a system of two interacting atoms, where each atom presents one free electron. The resolution of this tow sites problem is done by the SCRPA approximation; our calculations allow as studying the intersite interaction effect on the excitation energies of system. We have showed that the attractive interaction between the electrons of the neighbour’s atoms is the origin of supplementary conductivity of the system.
Using the SCRPA, we study the intersite interaction effect on the dynamics of N electrons system. We have considered an extended Hubbard model including intrasite and intersite interactions, and we have applied this model to a system of two neighbouring atoms containing a free electron. The application of SCRPA to this model allows us to study the intersite interaction effect on the ground state and the excitation energies of system. We show that the repulsive interaction between the electrons of the neighbouring atoms is the origin of an supplementary conductivity of the system.
The self consistent random phase approximation (SCRPA) and a direct analytical (DA) method are proposed to solve the Extended Hubbard Model (EHM) in one dimension (1D). We have considered an EHM including on-site and off-site interactions for closed chains in 1D with periodic boundary conditions. The comparison of the SCRPA results with the ones obtained by a DA approach shows that the SCRPA treats the problem of these closed chains in a rigorous manner. The analysis of the nearest–neighbour repulsion effect on the dynamics of our closed chains shows that this repulsive interaction between the electrons of the neighbouring atoms induces supplementary conductivity, since, the SCRPA energygap vanishes when these closed chains are governed by a strong repulsive on-site interaction and intermediate nearest–neighbour repulsion.
We are interested in the possibility that a generalization of Self Consistent Random Phase Approximation (SCRPA) to the Extended Hubbard Model can lead us to accurate estimations of the ground state energy, for closed chains in one dimension with periodic boundary conditions: N=2 (two states problem). We have considered an extended Hubbard model including on-site and off-site interactions, we have compared the SCRPA with a Direct Analytical(DA) results for the ground state energy, and have shown that SCRPA solves the two states problem exactly for any value of U (on-site interaction energy), V2 (off-site interaction energy with opposite spins) and (off-site interaction energy with same spins).
Within the one-dimensional Hubbard model linear closed chains with various numbers of sites are considered in the self-consistent random phase approximation (SCRPA). Excellent results with a minimal numerical effort are obtained for (2+4n)(2+4n)(2+4n)-site cases, confirming earlier results with this theory for other models. However, the 4n4n4n-site cases need further consideration. The SCRPA solves the two-site problem exactly. It therefore contains the two-electron and high-density Fermi gas limits correctly.
Abstract Collective excitations in the superconducting state of an extended Hubbard model with an intrasite attraction are investigated using the random phase approximation method. The results for the energy of gapless excitations are consistent with the well known result of Anderson in the limit of weak attraction and the result of the perturbation theory (with respect to the band term) in the limit of strong attraction. Investigating the dependence of the excitation energy on the density of electrons in the band conditions are found of instability of the singlet superconducting state with respect to the disordered state (for attractive intersite interactions) and to the charge ordered superconducting state (for intersite repulsion).