Continuous topological phase transitions between clean quantum Hall states

Continuous transitions between states with the {\em same} symmetry but different topological orders are studied. Clean quantum Hall (QH) liquids with neutral quasiparticles are shown to have such transitions. For clean bilayer (nnm) states, a continous transition to other QH states (including non-Abelian states) can be driven by increasing interlayer repulsion/tunneling. The effective theories describing the critical points at some transitions are derived.