Fractional quantum Hall junctions and two-channel Kondo models

A mapping between fractional quantum Hall (FQH) junctions and the two-channel Kondo model is presented. We discuss this relation in detail for the particular case of a junction of a FQH state at (formula presented) and a normal metal. We show that in the strong coupling regime this junction has a non-Fermi-liquid fixed point. At this fixed point the electron Green’s function has a branch cut and the impurity entropy is equal to (formula presented) We construct the space of perturbations at the strong coupling fixed point and find that the dimension of the tunneling operator is (formula presented) These properties are strongly reminiscent of the non-Fermi-liquid fixed points of a number of quantum impurity models, particularly the two-channel Kondo model. However we have found that, in spite of these similarities, the Hilbert spaces of these two systems are quite different. In particular, although in a special limit the Hamiltonians of both systems are the same, their Hilbert spaces are not since they are determined by physically distinct boundary conditions. As a consequence the spectrum of operators in the two problems is different.