Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1997-01-30
Nucl.Phys. B498 (1997) 513-538
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
37 pages, LaTeX. Some references added, minor changes at the end of section V
Scientific paper
10.1016/S0550-3213(97)00351-9
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 $c=-2$ 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 $c=-2$ theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the $c=1$ chiral Dirac fermion, which is related in a simple way to the $c=-2$ theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the $SU(2)$ 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.
Flohr Michael
Gurarie Victor
Nayak Chetan
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