We describe the braiding statistics of topological twist defects in fractional quantum Hall (FQH) states. In particular, we study Abelian bosonic
(mmn) FQH states with bilayer symmetries. Twist defects are staircases that lift orbiting quasiparticles from one layer to another. These point defects exhibit semiclassical non-Abelian characteristics. We develop a procedure to evaluate consistent basis transformations (
F symbols) of the defect fusion theory. Unlike quantum anyonic excitations of a topological phase, the exchange and braiding statistics of twist defects is not characterized by modular transformations, but instead a subcollection known as congruent transformations. We also characterize the projective nature of unitary braiding operations and relate it to the global
Z2 bilayer symmetry.
Following a suggestion given in Cristofano et al (2003 Phys. Lett. B 571 250; 2004 Nucl. Phys. B 679 621), we show how a bilayer quantum Hall system at fillings ν = m /( pm + 2) can exhibit a point-like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings of Deviatov et al (2005 Phys. Rev. B 72 041305) which evidence the presence of a topological defect in the bilayer system.