Thermodynamic Bethe-ansatz equations for the Hubbard chain with an attractive interaction

The thermodynamic Bethe-ansatz equations for the one-dimensional Hubbard model are derived for an attractive on-site interaction of the electrons, extending in this way Takahashis result for the repulsive Hubbard chain. The results are discussed in several special limits, e.g., interaction much larger than the hopping, U'0 case, and the high- and low-temperature limits. The dominating states at low temperatures consist of spin-paired electrons (resembling Cooper pairs) and bound states of such pairs. The excitation spectrum and its properties are discussed in the context of superconductivity and resonant valence bonds.