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An exact analytical diagonalization is used to solve the two dimensional Extended Hubbard Model for system with finite size. We have considered an Extended Hubbard Model (EHM) including on-site and off-site interactions with interaction energy U and V respectively, for square lattice containing 4*4 sites at one-eighth filling with periodic boundary conditions, recently treated by Kovacs et al [1]. Taking into account the symmetry properties of this square lattice and using a translation linear operator, we have constructed a r-space basis, only, with 85 state-vectors which describe all possible distributions for four electrons in the 4*4 square lattice. The diagonalization of the 85*85 matrix energy allows us to study the local properties of the above system as function of the on-site and off-site interactions energies, where, we have shown that the off-site interaction encourages the existence of the double occupancies at the first exited state and induces supplementary conductivity of the system., Comment: 10 pages, 5 figures; IOP Publishing

When interfaces between ordered domains are ordered clusters, frustration disappears. A phase with mixed ordered structures emerges but no length scale can be associated to. We show that sum of densities of each structure plays the role of order parameter. For, we consider a regular half full lattice with repulsive interaction extended to second neighboring particles. Ordered structures are p(2X2) when ratio between second and first neighboring interaction energies R=J SN /J FN <0.5 and degenerate p(2X1)/p(1X2) for R>0.5. The ground states coexist with another named p(4X2)/p(2X4) at central bi-critical point: a state to cross when passing between non-frustrated ordered phases.

The Self Consistent Random Phase Approximation (SCRPA) and a Direct Analytical (DA) method are proposed to solve the Extended Hubbard Model in 1D. We have considered an Extended Hubbard Model (EHM) including on-site and off-site interactions for closed chains in one dimension with periodic boundary conditions. The comparison of the SCRPA results with ones obtained by a Direct Analytical approach shows that the SCRPA treats the problem of these closed chains with 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 energy gap vanishes when these closed chains are governed by a strong repulsive on-site interaction and intermediate nearest-neighbour repulsion., Comment: 9 pages, 4 figures

Langevin simulations provide an effective way to study collective effects of Brownian particles immersed in a two-dimensional periodic potential. In this paper, we concentrate essentially on the behaviour of the tracer (DTr) and bulk (DB) diffusion coefficients as function of friction. Our simulations show that in the high friction limit, the two physical quantities DTr and DB present qualitatively the same behaviour, for both coupled and decoupled substrate potentials. However, for the low friction regime, and especially for the coupled potential case, an anomalous diffusion behaviour is found. We also found that in the case of weak dynamical coupling between the ad-particles and the substrate, the exponents are not universal and rather depend on the potentials. Moreover, changes in the inter-particle potentials may reverse the behaviour to a normal one.

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., Comment: 8 pages