Finite-Size Studies on the SO(5) Symmetry of the Hubbard Model

We present numerical evidence for the approximate SO(5) symmetry of the Hubbard model on a 10-site cluster. Various dynamic correlation functions involving the $\pi$ operators, the generators of the SO(5) algebra, are studied using exact diagonalization, and are found to possess sharp collective peaks. Our numerical results also lend support to the interpretation of the recent resonant neutron scattering peaks in the YBCO superconductors in terms of the Goldstone modes of the spontaneously broken SO(5) symmetry. Perturbations such as longer-ranged hoppings and interactions do not suppress the $\pi$ resonance in interesting parameter regimes.