Thermodynamic Bethe ansatz equations of one-dimensional Hubbard model and high-temperature expansion

A numerical method to calculate thermodynmic Bethe ansatz equations is proposed based on Newton's method. Thermodynamic quantities of the one-dimensional Hubbard model are numerically calculated and compared with high-temperature expansion and numerical results of the quantum transfer matrix method by Juttner, Klumper, and Suzuki. The coincidence is surprisingly good. We obtain the high-temperature expansion of the grand potential up to beta(6).