Transition from Integer Quantum Hall State to Insulator

We study disorder induced transition between quantum Hall states and insulator state in a {\it lattice} model. We find the positions of the extended states do not change as disorder strength is varied. As a consequence, there are direct transitions from all Landau level quantum Hall states to insulator states, in contrast to the global phase diagram from early studies based on continuous models. We also provide the microscopic understanding of the transition in terms of the topological properties of the system.