MOTT TRANSITION IN AN ANYON GAS

We introduce and analyze a lattice model of anyons in a periodic poten tial and an external magnetic field, which exhibits a transition from a Mott insulator to a quantum Hall fluid. The transition is characteri zed by the anyon statistics alpha, which can vary between fermions, al pha = 0, and bosons, alpha = 1. For bosons the transition is in the un iversality class of the classical three-dimensional XY model. Near the fermion limit, the transition is described by a massless 2 + 1 Dirac theory coupled to a Chern-Simons gauge field. Analytic calculations pe rturbative in alpha, and also a large-N expansion, show that due to ga uge fluctuations, the critical properties of the transition are depend ent on the anyon statistics. Comparison with previous calculations at and near the boson limit, strongly suggest that our lattice model exhi bits a fixed line of critical points, with universal critical properti es that vary continuosly and monotonically as one passes from fermions to bosons. Possible relevance to experiments on the transitions betwe en plateaus in the fractional quantum Hall effect and the magnetic-fie ld-tuned superconductor-insulator transition are briefly discussed.