The spin-$3/2$ fermion models with contact interactions have a generic SO(5) symmetry without any fine-tuning of parameters. Its physical consequences are discussed in both the continuum and lattice models. A Monte Carlo algorithm free of the sign problem at any doping and lattice topology is designed when the singlet and quintet interactions satisfy $U_0\le U_2\le -\frac{3}{5}{U}_0$ $(U_0\le 0)$, thus making it possible to study different competing orders with high numerical accuracy. This model can be accurately realized in ultracold atomic systems.

• Received 12 February 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.186402