Can classical orders coexist with quantum orders?

Question

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

Comments

In my books the classical orders emerge from the quantum mechanical orders. In other words the basic level is quantum mechanical and the classical is a limiting case macroscopically. Coexist does not describe the relationship accurately.

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

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@ anna v, can you give me a link to your books? Thank you.

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

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I am sorry, it is just an english expession "in my books". I can give you a link to Motl's blog where he shows how from photons one gets the classical electromagnetic field: motls.blogspot.gr/2011/11/…

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