Quantum Hall Bilayers and the Chiral Sine-Gordon Equation

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.

revtex, epsf; 39 p., 4 figs; corrections to three equations; two-up postscript at http://www.sns.ias.edu/~leonid/csg-2up.ps

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• Partial equilibration of anti-Pfaffian edge modes at $\nu =5/2$
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Probing Spin-Charge Separation in Tunnel-Coupled Parallel Quantum Wires
• Conductance oscillations in strongly correlated fractional quantum Hall line junctions
• The fractional quantum Hall effect in infinite layer systems
• Paired states on a torus
• Strongly Correlated Fractional Quantum Hall Line Junctions
• Notes on Infinite Layer Quantum Hall Systems
• Correlated tunneling and the instability of the fractional quantum Hall edge
• Tunnelling Effects in a Brane System and Quantum Hall Physics
• Jain states on a torus: an unifying description
• Localization and conductance in fractional quantum Hall edges
• Edge Dynamics in Quantum Hall Bilayers II: Exact Results with Disorder and Parallel Fields
• Comment on "Strongly correlated Fractional Quantum Hall line junction"
• Electrostatics of Edge States of Quantum Hall Systems with Constrictions: Metal--Insulator Transition Tuned by External Gates
• Metal-Insulator Transition Tuned by External Gates in Hall Systems with Constrictions
• The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems
• Manifestation of edge-bulk incompatibility in fractional quantum Hall platform
• Tunneling between coupled Luttinger liquids
• Langevin Simulation of the Chirally Decomposed Sine-Gordon Model