Superconducting Fluctuations in the Hubbard Model With an Attractive On-Site Interaction in One Dimension

The low-temperature thermodynamics of the one-dimensional Hubbard model with attractive on-site interaction of the electrons is discussed with the framework of the Bethe ansatz for the wave function. At low T the dominant states consist of spin-paired electrons (Cooper-pair-like) and excitations of such pairs (without breaking up the singlet bound states). A critical field H sub c (energy required to depair a Cooper pair) is obtained at T = 0 (note that the superconducting T sub c = 0), which disappears for T not = 0. There is no magnetic response at T = 0 for H < H sub c . The one-electron correlation function falls off exponentially with distance, while the singlet pair--singlet pair correlation decreases with a power law. The specific heat is linear in temperature, which is possibly a consequence of the dimension. The elementary excitations of the system are discussed. The excitation spectrum shows some analogies to that of resonant valence bonds in two dimensions. Graphs. 7 ref.--AA