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 /TV expansion. The transitions are found to be continuous in the large-TV limit and are described by a critical point that depends on a real parameter 0, 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-TV limit and shown to be 0 dependent.