Here our arguments are restricted to the realm of the Projective Symmetry Group(PSG) proposed by Prof. Wen,
Quantum Orders and Symmetric Spin Liquids. Xiao-Gang Wen. Phys. Rev. B 65 no. 16, 165113 (2002). arXiv:cond-mat/0107071.
and the following notations are the same as those in my previous question, Two puzzles on the Projective Symmetry Group(PSG)?.
When we say the projected physical spin state PΨ has some 'symmetry', e.g., translation symmetry, there will be two understandings:
(1) After a translation of the mean-field Hamiltonian H(ψi), say DH(ψi)D−1, the physical spin state is unchanged, say PΨ′∝PΨ, where Ψ′ is the ground state of the translated Hamiltonian DH(ψi)D−1.
(2) D(PΨ)∝PΨ.
I would like to know: are the above understandings equivalent to each other? Thanks in advance.
This post imported from StackExchange Physics at 2014-03-09 08:42 (UCT), posted by SE-user K-boy