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Degeneracy of non-Abelian quantum Hall states on the torus: domain walls and conformal field theory

Ardonne, Eddy and Bergholtz, Emil J. and Kailasvuori, Jaink and Wikberg, Emma (2008) Degeneracy of non-Abelian quantum Hall states on the torus: domain walls and conformal field theory. Journal of Statistical Mechanics: Theory and Experiment, 2008 (04). Art. No. P04016. ISSN 1742-5468. https://resolver.caltech.edu/CaltechAUTHORS:ARDjstme08b

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Abstract

We analyze the non-Abelian Read–Rezayi quantum Hall states on the torus, where it is natural to employ a mapping of the many-body problem onto a one-dimensional lattice model. On the thin torus—the Tao–Thouless (TT) limit—the interacting many-body problem is exactly solvable. The Read–Rezayi states at filling ν = k/(kM+2) are known to be exact ground states of a local repulsive k+1-body interaction, and in the TT limit this is manifested in that all states in the ground state manifold have exactly k particles on any kM+2 consecutive sites. For M\neq 0 the two-body correlations of these states also imply that there is no more than one particle on M adjacent sites. The fractionally charged quasiparticles and quasiholes appear as domain walls between the ground states, and we show that the number of distinct domain wall patterns gives rise to the nontrivial degeneracies, required by the non-Abelian statistics of these states. In the second part of the paper we consider the quasihole degeneracies from a conformal field theory (CFT) perspective, and show that the counting of the domain wall patterns maps one to one on the CFT counting via the fusion rules. Moreover we extend the CFT analysis to topologies of higher genus.


Item Type:Article
Additional Information:© 2008 IOP Publishing Ltd and SISSA. Received 13 February 2008, accepted for publication 19 March 2008. Published 14 April 2008. We wish to thank A Karlhede and H Hansson for fruitful discussions and for comments on this manuscript. We thank N Read for directing us to his discussion on the thin-torus limit in [30]. JK was supported by a grant from the Swedish Research Council.
Subject Keywords:conformal field theory; fractional QHE theory; quantum Hall effect
Issue or Number:04
Record Number:CaltechAUTHORS:ARDjstme08b
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:ARDjstme08b
Alternative URL:http://dx.doi.org/10.1088/1742-5468/2008/04/P04016
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10251
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:18 Apr 2008
Last Modified:03 Oct 2019 00:07

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