The SU(2) flux defined in the context of PSG is as follows:
Consider the mean-field Hamiltonian HMF=∑(ψ†iχijψj+H.c.) description of a 2D lattice spin-model, the definition of SU(2) flux PC for a loop C=i→j1→j2→...→jn→i with the base point i is PC=χij1χj1j2...χjni. On the other hand, the two SU(2) gauge-equivalent mean-field ansatz χij and χ′ij=GiχijG†j describe the same projected spin-wavefunction. And the SU(2) flux P′C for the same loop C is given by P′C=χ′ij1χ′j1j2...χ′jni=GiPCG†i, in general P′C≠PC, but an observable quantity should be invariant under the SU(2) gauge transformation χij→χ′ij=GiχijG†j,. Thus, does this mean that the SU(2) flux PC is not an observable quantity?
Thanks in advance.
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