By introducing a boundary condition for the quantum wire, the Hubbard model is solved exactly by means of the Bethe ansatz. The wave function for the bounded state is clearly defined, and the secular equation for the spectrum is exactly obtained. The ground state and low-lying excited states are studied in the thermodynamic limit. The ground-state energy in the strong coupling limit is obtained explicitly, and compared with the results of a periodic boundary condition.

The isotropic limit of spin systems with orbital degeneracy has global SU(4) symmetry. On many 2D lattices, the ground state does not possess long-range order, which may explain the observed spin liquid properties of LiNiO2. In the SU(4) N

The one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the SU(4) symmetric point by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a SU(4) singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.

A Hubbard-like model with SU(4) symmetry for electrons with two-fold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two electrons. The features of ground state and excited states for repulsive coupling are shown. For finite N number of electrons, the configurations of quantum numbers are given explicitly and the spectra of excitations are obtained by solving the Bethe-ansatz equation numerically. For infinite N, the ground state and various kinds of low-lying excitations are obtained on the basis of thermodynamics limit

The Hubbard model for electrons with orbital degeneracy is shown to have an underlying SUd(4) symmetry of spin-orbital double. A hidden charge SUc(4) symmetry is exposed and an extended Lieb-Mattis transformation, which maps these two symmetries into each other, is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a SO(6) Heisenberg magnet at half-filling and a SU(4) one at quarter-filling. The band is half-filled at all temperature for m53U/2. The features of ground-state and low-lying excitations in one dimension are indicated according to exact solutions.