Quantum orders in an exact soluble model

We find all the exact eigenstates and eigenvalues of a spin-1/2 model on square lattice: H=16gSigma(i)S(i)(y)S(i+(x) over cap)(x)S(i+(x) over cap+(y) over cap)(y)S(i+(y) over cap)(x).We show that the ground states for g<0 and g>0 have different quantum orders described by Z2A and Z2B projective symmetry groups. The phase transition at g=0 represents a new kind of phase transition that changes quantum orders but not symmetry. Both the Z2A and Z2B states contain Z(2) lattice gauge theories at low energies. They have robust topologically degenerate ground states and gapless edge excitations.