Off-site interaction effect in the Extended Hubbard Model with the SCRPA method

Abstract

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.

An exact solution to the extended Hubbard model in 2D for finite size system

“…2 shows that the energy E has a smooth U dependence and a linear V dependence. This behaviour is similar to the one obtained for the ground state energy of the chains Extended Hubbard Model with the Self Consistent Random Phase Approximation (SCRPA) [26], where we have also, defined the matrix energy but in the basis of vectors impulsion-space (k − space) and not in r − space representation. The curves of Figure 3: First excited state energy as function of U/t for different values of V /t Fig.…”

“…Despite being one of the most studied models to describe strongly the correlated electrons system, many questions concerning the Hubbard model remain as open problems. In [20], we have applied the self-consistent random phase approximation (SCRPA) [21,22] to solve the EHM in one-dimension (1D), where we have shown that this approach treats the correlations of closed chains in a rigorous manner. The behaviour of our SCRPA ground state and gap energies shows that the repulsive off-site interaction between the electrons of the neighbouring atoms induces the supplementary conductivity, since the SCRPA energy gap vanishes when the closed chains of the EHM are governed by a strong repulsive on-site and an intermediate repulsive off-site interaction.…”

Off-site interaction effect in the Extended Hubbard Model with SCRPA method

“…For more details, see Ref. [22]. In the present paper, we will compare these SCRPA solutions with ones obtained by a Direct Analytical approach for two local properties of our closed chain: the SCRPA ground state energy: E SCRP A GS = RP A| H II |RP A and the occupation number of states with spin σ and momenta k below the Fermi level :…”

“…In order to analyse the effect of V on the dynamics of our closed chains, we define the energy gap ∆ E as the difference between the first excited state energy ǫ 1 [22] and the ground state energy E SCRP A :…”