The Haldane-Rezayi Quantum Hall State and Conformal Field Theory
Abstract
We propose field theories for the bulk and edge of a quantum Hall state in the universality class of the Haldane-Rezayi wavefunction. The bulk theory is associated with the conformal field theory. The topological properties of the state, such as the quasiparticle braiding statistics and ground state degeneracy on a torus, may be deduced from this conformal field theory. The 10-fold degeneracy on a torus is explained by the existence of a logarithmic operator in the theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the chiral Dirac fermion, which is related in a simple way to the theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the symmetry -- which corresponds to the spin-rotational symmetry of the quantum Hall system -- is manifest and non-local. We make predictions for the current-voltage characteristics for transport through point contacts.
Keywords
Cite
@article{arxiv.cond-mat/9701212,
title = {The Haldane-Rezayi Quantum Hall State and Conformal Field Theory},
author = {V. Gurarie and M. Flohr and C. Nayak},
journal= {arXiv preprint arXiv:cond-mat/9701212},
year = {2009}
}
Comments
37 pages, LaTeX. Some references added, minor changes at the end of section V