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 (β̂). We obtain exact solutions for the spectra and correlation functions of the chiral sine-Gordon theory at the two values of β̂ at which electron tunneling in bilayers is not irrelevant. Of these, the marginal case (β̂2 = 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 (β̂2 ∋ e ℤ+) by the introduction of auxiliary degrees of freedom that could prove useful in other problems involving quantum Hall multi-layers.
Original language | English (US) |
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Pages (from-to) | 572-610 |
Number of pages | 39 |
Journal | Nuclear Physics B |
Volume | 565 |
Issue number | 3 |
DOIs | |
State | Published - Jan 24 2000 |
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics