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Quantum Hall Bilayers and the Chiral Sine-Gordon Equation

J. D. Naud·Leonid P. Pryadko·S. L. Sondhi
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Abstract

The edge state theory of a class of symmetric double-layer quantum Hall 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 form. 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). We obtain exact solutions for the spectra and correlation functions of the chiral sine-Gordon theory at the two values of beta at which the electron tunneling in bilayers is not irrelevant. Of these, the marginal case (beta^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 (integer beta^2) by the introduction of auxiliary degrees of freedom that could prove useful in other problems involving quantum Hall multilayers.

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J. D. Naud, Leonid P. Pryadko, S. L. Sondhi. 1999-12-02. Quantum Hall Bilayers and the Chiral Sine-Gordon Equation. https://doi.org/10.1016/s0550-3213(99)00658-6

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