2-BAND MODEL WITH ATTRACTIVE AND REPULSIVE INTERACTIONS IN ONE-DIMENSION - GROUND-STATE, EXCITATIONS, AND THERMODYNAMICS

We present the exact solution via Bethe's ansatz to an integrable mode l consisting of two parabolic bands of electrons of equal mass with a local delta-function exchange interaction. The interaction is attracti ve or repulsive depending on whether the interacting particles are in a spin-singlet or spin-triplet state. The structure of the Bethe ansat z and the classification of states is similar to the one of the two-ch annel Kondo problem. The interest in two-band models arises from the p ossibility that both the 3d(x2-y2) and 3d(x2) orbitals may play a role in high-T(c) cuprates. Some low-temperature properties of this model are discussed as a function of the interaction strength, a magnetic fi eld, and the (crystalline field) splitting between the bands. The attr active interaction leads to Cooper-pair-like bound states, which exist at every temperature. There is no long-range order and no condensatio n of the Cooper pairs. A threshold magnetic field is required to overc ome the binding energy of the Cooper pairs and there is no response to fields smaller than the critical one. The low-temperature specific he at is proportional to T, except at critical points (van Hove singulari ties of the bands) where C is-proportional-to T1/2 . The spectrum of e lemental excitations is approximately parabolic.