The Haldane-Rezayi quantum Hall state and conformal field theory |
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| Institution: | 1. Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA;2. Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA;1. Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, 3508 TD Utrecht, The Netherlands;2. Dipartimento di Scienze Fisiche e Chimiche, Università dell''Aquila, via Vetoio, I-67010 Coppito-L''Aquila, Italy;3. International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59012-970 Natal, Brazil;4. Department of Engineering Science and Physics, College of Staten Island, CUNY, Staten Island, NY 10314, USA;5. Physics program and Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, NY 10016, USA |
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| 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 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. |
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