Effective Interactions of the One-Dimensional d-p Model Based on the Luttinger Liquid Theory

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We examine effective interactions of the 1D d-p model mapped to a typical one-dimensional(1D) model such as the Hubbard model or the t-J model by the numerical diagonalization method combined with the Luttinger liquid theory. Analysis of the effective coupling constants of the mapped model gives the relationship between these models without ambiguity. We find that the renormalized interaction is relatively weak, though the repulsion of the d-p model at Cu-sites is very strong. We also find that the d-p model corresponds to not the t-J model but the Hubbard model for wide range of the parameters. It suggests that the Hubbard model is more favorable than the t-J model as a effective model of the d-p model in the low energy limit.

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