Luttinger-liquid parameter of Hubbard chain and Hubbard ladder models in the Hartree-Fock approximation

We investigate the Luttinger-liquid parameter K-p of the Hubbard chain and the Hubbard ladder models by the Hartree-Fock approximation combined with the Luttinger-liquid relation. By calculating the charge susceptibility Xe and the Drude weight D in the Hartree-Fock approximation, we can obtain K-p analytically. The form of K-p for the Hubbard chain is similar to that from the result of bosonization method and consistent with the exact result in the weak coupling region. Comparing the value of K-p for a finite system with the result of the numerical diagonalization method, we show that the result of K-p for the Hubbard ladder is also reliable in the weak coupling region. (C) 2000 Elsevier Science B.V. All rights reserved.