An exact solution to the Extended Hubbard Model in 2D for finite size system

TL;DR

This paper provides an exact analytical solution to the 2D Extended Hubbard Model on a finite 4x4 lattice, revealing how off-site interactions influence electron occupancy and conductivity.

Contribution

It introduces a symmetry-based basis construction and diagonalization approach for solving the finite 2D EHM, offering detailed insights into local properties and interactions.

Findings

Off-site interaction promotes double occupancy in the first excited state

Off-site interaction induces additional conductivity

Exact diagonalization method applied to finite 2D lattice

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.