Twisted CFT and bilayer Quantum Hall systems

TL;DR

This paper explores the conformal field theory description of bilayer Quantum Hall systems, focusing on impurity interactions, pairing symmetry, and fixed points, revealing complex impurity dynamics and phase transitions.

Contribution

It identifies impurity interactions in a CFT model of bilayer Quantum Hall systems and analyzes their effects on fixed points and phase stability.

Findings

Impurity interactions are characterized by boundary terms resembling Kondo tunneling.

An anomalous fixed point exists at finite coupling, unstable under unbalance.

Flow to a vacuum state with no quasi-holes occurs at instability.

Abstract

We identify the impurity interactions of the recently proposed CFT description of a bilayer Quantum Hall system at filling nu =m/(pm+2) in Mod. Phys. Lett. A 15 (2000) 1679. Such a CFT is obtained by m-reduction on the one layer system, with a resulting pairing symmetry and presence of quasi-holes. For the m=2 case boundary terms are shown to describe an impurity interaction which allows for a localized tunnel of the Kondo problem type. The presence of an anomalous fixed point is evidenced at finite coupling which is unstable with respect to unbalance and flows to a vacuum state with no quasi-holes.