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

Abstract

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.

Exact Diagonalization Study of an Extended Hubbard Model for a Cubic Cluster at Quarter Filling

“…The Hubbard model and its extensions, being fundamental models for strongly correlated systems, still constitute a challenge and their thermodynamics attracts considerable attention [1][2][3][4][5][6][7][8][9]. The exact thermodynamic solutions are known only for a limited range of systems, including zero-dimensional ones, for which exact diagonalization can be performed [10][11][12][13][14][15], albeit this approach requires significant computational resources.…”