Similarities between the t-J and Hubbard models in weakly correlated regimes
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We present a comparative study of the Hubbard and t - J models far away from half-filling. We show that, at such fillings the t - J Hamiltonian can be seen as an effective model of the repulsive Hubbard Hamiltonian over the whole range of correlation strength. Indeed, the | t/U| ∈\(\)0, + ∞\(\) range of the Hubbard model can be mapped onto the finite range | J/t| ∈\(\)2, 0\(\) of the t - J 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 J = - 2| t| and the infinitely correlated U = + ∞ 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 t - J Hamiltonian in low-filled systems can therefore be a good alternative to the Hubbard model in large time-consuming calculations.
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