Quantum Hall bilayers and the chiral sine-Gordon equation

The edge state theory of a class of symmetric double-layer quantum Wall systems with interlayer electron tunneling reduces to the sum of a free field theory and a field theory of a chiral Bose field with a self-interaction of the sine-Gordon farm, We argue that the perturbative renormalization group flow of this chiral sine-Gordon theory is distinct from the standard (non-chiral) sine-Gordon theory, contrary to a previous assertion by Renn, and that the theory is manifestly sensible only at a discrete set of values of the inverse period of the cosine interaction (<(beta)over cap>). we obtain exact solutions for the spectra and correlation functions of the chiral sine-Gordon theory at the two values of <(beta)over cap> at which electron tunneling in bilayers is not irrelevant. Of these, the marginal case (<(beta)over cap>(2) = 4) is of greatest interest: the spectrum of the interacting theory is that of two Majorana fermions with different, dynamically generated, velocities. For the experimentally observed bilayer 331 state at filling factor 1/2, this implies the trifurcation of electrons added to the edge. We also Present a method for fermionizing the theory at the discrete points (<(beta)over cap>(2) is an element of Z(+)) by the introduction of auxiliary degrees of freedom that could prove useful in other problems involving quantum Wall multi-layers. (C) 2000 Elsevier Science B.V. All rights reserved.