Tomorrow I am giving a seminar in the Physics Department at the Indian Institute of Science in Bangalore. The talk "Emergent states of quantum matter" is similar to the one I gave two weeks ago at JNCASR.
Then an interesting question was raised. "There are two complementary pictures of the quasi-particles in the Fractional Quantum Hall Effect: composite fermions and fractionally charged anyons. Can one explicitly show they are equivalent?"
I am not sure. One can certainly show that the overlap of the relevant variational wave functions, Laughlin's and the composite fermion ones, is significant and that for small systems that the overlap of both of these wave functions with exact numerical wave function.
However, that "black box" proof is not quite the same as establishing "adiabatic continuity" between the two different representations. Has anyone explicitly done that?
I welcome other answers to this question.