Eur. Phys. J. B 28, 49-54 (2002)
https://doi.org/10.1140/epjb/e2002-00198-5

Similarities between the t-J and Hubbard models in weakly correlated regimes

¹ Laboratoire de Physique Quantique, IRSAMC, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 4, France
² Laboratoire de Structure et Dynamique des Systèmes Moléculaires et Solides, USTL II, bâtiment 15, CC-014, 34095 Montpellier Cedex 5, France

Corresponding author: ^a Marie@irsamc.ups-tlse.fr

Received: 22 February 2002
Revised: 6 May 2002
Published online: 9 July 2002

Abstract

We present a comparative study of the Hubbard and models far away from half-filling. We show that, at such fillings the Hamiltonian can be seen as an effective model of the repulsive Hubbard Hamiltonian over the whole range of correlation strength. Indeed, the range of the Hubbard model can be mapped onto the finite range of the model, provided that the effective exchange parameter J is defined variationally as the local singlet-triplet excitation energy. In this picture the uncorrelated limit U=0 is associated with the super-symmetric point and the infinitely correlated limit with the usual J=0 limit. A numerical comparison between the two models is presented using different macroscopic and microscopic properties such as energies, charge gaps and bond orders on a quarter-filled infinite chain. The usage of the Hamiltonian in low-filled systems can therefore be a good alternative to the Hubbard model in large time-consuming calculations.