Continuous Topological Phase Transitions between Clean Quantum Hall States

Continuous transitions between states and the same symmetry but different topological orders are studied. Clean quantum Hall (QH) liquids with neutral nonbosonic quasiparticles are shown to have such transitions under the right conditions. For clean bilayer $\left(\mathrm{mmn}\right)$ states, a continuous 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 obtained.