Fractional quantum Hall junctions and two-channel Kondo models

Abstract

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 $\ensuremath{\nu}=1/3$ 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 $S=\frac{1}{2}\mathrm{ln}2.$ We construct the space of perturbations at the strong coupling fixed point and find that the dimension of the tunneling operator is $\frac{1}{2}.$ 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.