TBA Equations of 1D Hubbard Model and High-Temperature Expansion

New numerical method to calculate thermodynmic Bethe ansatz equations is proposed based on Newton’s method. Thermodynamic quantities of one-dimensional Hubbard model is numerically calculated and compared with high temperature expansion and numerical results of quantum transfer matrix method by J"uttner, Kl"umper and Suzuki. The coincidence is surprisingly good. We get high-temperature expansion of grand potential up to ${\beta }^6$.