Exact SO(5) symmetry in the spin-3/2 fermionic system

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)less than or equal toU(2)less than or equal to-3/5 U-0 (U(0)less than or equal to0), thus making it possible to study different competing orders with high numerical accuracy. This model can be accurately realized in ultracold atomic systems.