This question is a very good question, which is partially addressed in my original article on PSG:

arXiv:cond-mat/0107071 *Quantum Orders and Symmetric Spin Liquids*

arXiv:cond-mat/0110397 *Quantum Order: a Quantum Entanglement of Many Particle*

arXiv:cond-mat/0202166 *Gapless Fermions and Quantum Order*

One can partially and indirectly measure PSG by measure the spectrum function
of spin correlation (which is a two spinon spectral function). In π flux state, $T_xT_y=−T_yT_x$, the lower edge of the spectral function
is repeated in 1/4 of BZ. (See Fig. 11 of arXiv:cond-mat/0107071, for example)

This post imported from StackExchange Physics at 2014-04-11 15:49 (UCT), posted by SE-user Xiao-Gang Wen