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FizA

Ground State Energy of 2d Extended Hubbard Model for Finite Size System with AN Exact Diagonalization

Coden Fizae, Said Harir, Mohamed Bennai, Y. Boughaleb

Published Jan 1, 2008• 0 citations
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Abstract

Using an exact analytical diagonalization for an extended Hubbard model, we study the first nearest-neighbour repulsion effect on the behaviour of a two-dimensional system of finite size at low density of electrons. The obtained results show that the introduction of the nearest-neighbour off-site interaction allows the correlation effects to become more remarkable and to play an essential role in the electron dynamics, and this off-site interaction encourages the formation of double occupancies.

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Using an exact analytical diagonalization for an extended Hubbard model, we study the first nearest-neighbour repulsion effect on the behaviour of a two-dimensional system of finite size at low density of electrons. The obtained results show that the introduction of the nearest-neighbour off-site interaction allows the correlation effects to become more remarkable and to play an essential role in the electron dynamics, and this off-site interaction encourages the formation of double occupancies.
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We investigate the ground state phase diagram of the two dimensional Extended Hubbard Model (EHM) with more than Nearest-Neighbor (NN) interactions for finite size system at low concentration. This EHM is solved analytically for finite square lattice at one-eighth filling. All eigenvalues and eigenvectors are given as a function of the on-site repulsion energy U and the off-site interaction energy Vij. The behavior of the ground state energy exhibits the emergence of phase diagram. The obtained results clearly underline that interactions exceeding NN distances in range can significantly influence the emergence of the ground state conductor–insulator transition.
An exact-diagonalization technique on small clusters is used to study the ground states and single-particle excitations of the Hubbard model with on-site (U) and nearest-neighbor (V) Coulombic repulsive interactions. It is shown that the long-range charge-density-wave state realized in a half-filled two-dimensional square lattice for 4V\ensuremath{\gtrsim}U persists up to quarter filling, and that the doped carriers form a small Fermi surface that encloses an area corresponding to the number of doped carriers rather than the total number of electrons involved in the system. The present result offers a well-defined counterexample in the discussion of the Fermi-surface dimensions of strongly correlated electron systems, and may provide a complementary understanding of the large Fermi surface believed to exist in the ordinary Hubbard model.
An extended Hubbard model that includes not only on-site but also intersite Coulomb repulsion and distant transfer is numerically investigated using the exact Lanczos diagonalization method for finite-size systems up to L=20L=20L=20 sites. The aim is to study the charge order and unconditional dimerization of a chain at density $\ensuremath{\rho}=0.4$. From the analysis of the spin and charge correlation functions, we deduce the formation of a dimer insulating state which is a Wigner lattice-type charge ordered state. The next-nearest-neighbor hopping t2{t}_{2}t2​ enhances the intradimer correlations and weakens the interdimer correlations. Implications for the CuO2\mathrm{Cu}{\mathrm{O}}_{2}CuO2​ chains in Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ are discussed.