Thursday, 12 December 2019

condensed matter - Is the SU(2) flux defined in the context of Projective Symmetry Group(PSG) an observable quantity?


The SU(2) flux defined in the context of PSG is as follows:


Consider the mean-field Hamiltonian HMF=(ψiχijψj+H.c.) description of a 2D lattice spin-model, the definition of SU(2) flux PC for a loop C=ij1j2...jni with the base point i is PC=χij1χj1j2...χjni. On the other hand, the two SU(2) gauge-equivalent mean-field ansatz χij and χij=GiχijGj describe the same projected spin-wavefunction. And the SU(2) flux PC for the same loop C is given by PC=χij1χj1j2...χjni=GiPCGi, in general PCPC, but an observable quantity should be invariant under the SU(2) gauge transformation χijχij=GiχijGj,. Thus, does this mean that the SU(2) flux PC is not an observable quantity?


Thanks in advance.




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