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Analytical Results of the One-Dimensional Hubbard Model in the High Temperature Limit

We investigate the grand potential of the one-dimensional Hubbard model in the high temperature limit, calculating the coefficients of the high temperature expansion ($β$-expansion) of this function up to order $β^4$ by an alternative method. The results derived are analytical and do not involve any perturbation expansion in the hopping constant, being valid for arbitrary density of electrons in the one-dimensional model. In the half-filled case, we compare our analytical results for the specific heat and the magnetic susceptibility, in the high-temperature limit, with the ones obtained by Beni {\it et al.} and Takahashi's integral equations, showing that the latter result does not take into account the complete energy spectrum of the one-dimensional Hubbard model. The exact integral solution by Jüttner {\it et al}. is applied to the determination of the range of validity of our expansion in $β$ in the half-filled case, for several different values of $U$.