Numerical evidence for SO(5) symmetry and superspin multiplets in the two-dimensionalt−Jmodel

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-$T_c$ 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.