The grand potential of the one-dimensional extended Hubbard model up to order β5

We apply the method of Rojas et al. (J. Math. Phys. 43 (2002) 1390) to calculate the high-temperature expansion of the grand potential of the one-dimensional (1-D) extended Hubbard model up to order β5 for arbitrary chemical potential. The analytic expansion derived is valid for positive and negative values of U and V. From the β-expansion of the grand potential we obtain an approximate temperature-dependent expansion for the chemical potential for the quarter-filled band. We study the high-temperature behavior of the thermodynamical quantities, in the quarter-filled band, at different phases of the extended Hubbard model. Finally, we extend the comparison of the thermodynamic properties of the 1-D extended Hubbard model with composite spin-1 model (Phys. Rev. B 34 (1986) 487; Phys. Rev. B 40 (1989) 7150) to lower temperatures. We show that the specific heat and the average energy per spin of the composite spin model, in the high temperature region, cannot be well approximated by the respective thermodynamic functions of the one-dimensional extended Hubbard model, even in the strong-U regime.