Critical points in edge tunneling between generic FQH states

Abstract

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 at the boundary gives a nontrivial consistency condition for possible low-energy boundary conditions. The effect of interactions and random hopping on fixed points is studied through a perturbative RG approach which generalizes the Giamarchi-Schulz RG for disordered Luttinger liquids to broken left-right symmetry and multiple modes. The allowed termination points of a multicomponent edge are classified by a B-matrix with rational matrix elements. 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. The correlation functions of electronlike operators across a junction are found from the B matrix using a simple image-charge description, along with the induced lattice of boundary operators. Many of the results obtained are also relevant to ordinary Luttinger liquids.