For example, the ground state of the antiferromagnetic(AFM) Heisenberg model $H=J\sum_{<ij>}\mathbf{S}_i \cdot \mathbf{S}_j(J>0)$ on a 2D square lattice is a Neel state, which is a classical order described by conventional order parameters $\left \langle \mathbf{S}_i \right \rangle$.

On the other hand, if we use the Schwinger-fermion mean-field theory to study $H$, we will get a mean-field Hamiltonian $H_{MF}=\sum (f_i^\dagger \chi_{ij} f_j+f_i^\dagger \eta_{ij} f_j^\dagger+H.c.)$ which is studied in Wen's papers of PSG, and now we can study the PSG of the mean-field ansatz $(\chi_{ij},\eta_{ij})$ and associated quantum order.

So according to the above example, can we say that the AFM SDW phase(classical order) *possesses* the quantum order(PSG)? Thank you very much.

This post imported from StackExchange Physics at 2014-03-09 08:43 (UCT), posted by SE-user K-boy