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29 March 2024
 
  » arxiv » cond-mat/9701212

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The Haldane-Rezayi Quantum Hall State and Conformal Field Theory
V. Gurarie ; M. Flohr ; C. Nayak ;
Date 30 Dec 1996
Journal Nucl.Phys. B498 (1997) 513-538
Subject Mesoscopic Systems and Quantum Hall Effect | cond-mat.mes-hall hep-th
AffiliationIAS), M. Flohr (IAS), C. Nayak (ITP
AbstractWe 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.
Source arXiv, cond-mat/9701212
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