Generalized Valence Bond State and Solvable Models for Spin-1/2 Systems with Orbital degeneracy

A spin-1/2 system with double orbital degeneracy may possess SU(4) symmetry. According to the group theory a global SU(4) singelt state can be expressed as a linear combination of all possible configurations consisting of four-site SU(4) singlets. Following P. W. Andersion's idea for spin 1/2 system, we propose that the ground state for the antiferromagnetic SU(4) model is SU(4) resonating valence bond (RVB) state. A short-range SU(4) RVB state is a spin and orbital liquid, and its elementary excitations has an energy gap. We construct a series of solvale models which ground states are short-range SU(4) RVB states. The results can be generalized to the antiferromagnetic SU(N) models.