Unambiguous relationship between the Hubbard, t-J and d-p models in one-dimension based on the Luttinger liquid theory

We examine the one-dimensional (1D) d-p model in comparison with typical 1D models such as the 1D Hubbard model and the 1D t-J model using the numerical diagonalization method combined with the Luttinger liquid theory. We calculate the spin velocity vσ, the charge velocity vρ and the Luttinger liquid parameter Kρ for each model. Using these parameters, a relationship between the models is obtained unambiguously. We find that the d-p model can be described by the Hubbard model in the wide parameter region, while it can be described by the t-J model only in the strong coupling limit