Numerical evidence for SO(5) symmetry and superspin multiplets in the two-dimensional t-J model

In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization we verify that low-energy states of the t-J Model, a widely used microscopic model for the high-ir, cuprates, form SO(5) symmetry multiplets. Our results show that the d-wave superconducting ground states away from half-filling are obtained from the higher-spin states at half-filling through SO(5) rotations. The SO(5) symmetry is found to be robust against the inclusion of longer-ranged Coulomb repulsion and next-nearest-neighbor hopping.