Transitions between the quantum Hall states and insulators induced by periodic potentials

Transitions between two quantum Hall states or between a quantum Hall state and a Mott insulator induced by periodic potentials are studied in the 1/N expansion. The transitions are found to be continuous in the large-N limit and are described by a critical point that depends on a real parameter θ, which is determined by the topological orders in the quantum Hall states involved in the transition. Some critical exponents and universal quantities are calculated in the large-N limit and shown to be θ dependent.