  We propose quantum phase transitions beyond the Landau's paradigm of Sp(4)
spin Heisenberg models on the triangular and square lattices, motivated by the
exact Sp(4)$\simeq$ SO(5) symmetry of spin-3/2 fermionic cold atomic system
with only $s-$wave scattering. On the triangular lattice, we study a phase
transition between the $\sqrt{3}\times\sqrt{3}$ spin ordered phase and a $Z_2$
spin liquid phase, this phase transition is described by an O(8) sigma model in
terms of fractionalized spinon fields, with significant anomalous scaling
dimensions of spin order parameters. On the square lattice, we propose a
deconfined critical point between the Neel order and the VBS order, which is
described by the CP(3) model, and the monopole effect of the compact U(1) gauge
field is expected to be suppressed at the critical point.
