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arXiv:hep-th/0108173 · Nuclear Physics B

The ν=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between Abelian and non-Abelian statistics

Lachezar S. Georgiev

Published Feb 1, 2003• 17 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(02)01076-3

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We review a recent development in the theoretical understanding of the nu=5/2 quantum Hall plateau and propose a new conformal field theory, slightly different from the Moore-Read one, to describe a new universality class of this plateau. The ground state is still given by the Pfaffian and is completely polarized, however, the elementary quasiholes are charge 1/2 anyons with abelian statistics theta=pi/2, which obey complete spin-charge separation. The physical hole is represented by two such quasiholes plus a free neutral Majorana fermion. The edge spectrum of the new state is symmetric with respect to the particle-hole transformation. Finally, we find indications of a two-step phase transition between the new and the Moore-Read states, through a compressible state, which is characterized by spontaneous breaking of the charge conjugation symmetry.
We propose a one-parameter variational ansatz to describe the tunneling-driven Abelian to non-Abelian transition in bosonic ν=1/2+1/2 fractional quantum Hall bilayers. This ansatz, based on exact matrix product states, captures the low-energy physics all along the transition and allows us to probe its characteristic features. The transition is continuous, characterized by the decoupling of antisymmetric degrees of freedom. We futhermore determine the tunneling strength above which non-Abelian statistics should be observed experimentally. Finally, we propose to engineer the interlayer tunneling to create an interface trapping a neutral chiral Majorana fermion. We microscopically characterize such an interface using a slightly modified model wave function.