A general description of weak and strong tunneling fixed points is developed in the chiral-Luttinger-liquid model of quantum Hall edge states. Tunneling fixed points are a subset of “termination” fixed points, which describe boundary conditions on a multicomponent edge. The requirement of unitary time evolution for bounded edges gives a nontrivial consistency condition for possible low-energy boundary conditions. The effects of interactions and random hopping on fixed points are studied through a perturbative renormalization-group (RG) approach which generalizes the Giamarchi-Schulz RG for disordered Luttinger liquids to broken left-right symmetry and multiple modes. We apply our approach to a number of examples, such as tunneling between a quantum Hall edge and a superconductor and tunneling between two quantum Hall edges in the presence of interactions. Interactions are shown to induce a continuous renormalization of effective tunneling charge for the integrable case of tunneling between two Laughlin states.

• Received 25 June 2001

DOI:https://doi.org/10.1103/PhysRevB.66.115305