Equivalence of fractional quantum Hall and resonating-valence-bond states on a square lattice

Abstract

We show that a fractional quantum Hall state is equivalent to one particular resonating-valence-bond (RVB) state, the ``flux phase'' on a square lattice. The fictitious magnetic flux is dynamically generated in the RVB state. The fractional quantum Hall wave function for the flux phase is explicitly shown to be a singlet.