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Non-Abelian quantum Hall states of fermions and bosons

N. Read

Bulletin of the American Physical SocietyMar 5, 20070 citations

Conformal Field Theory Approach to Abelian and Non-Abelian Quantum Hall Quasielectrons

T. H. Hansson, Maria Hermanns, Nicolas Regnault +1 more

The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.

arXiv:0810.0636Physical Review LettersApr 23, 200938 citations

Non-abelian Quantum Hall States on the

Thin Torus

Jan 1, 20090 citations

Clustering Properties and Model Wave Functions for Non-Abelian Fractional Quantum Hall Quasielectrons

Bogdan Andrei Bernevig, F. D. M. Haldane

We present model wave functions for quasielectron (as opposed to quasihole) excitations of the unitary Z_{k} parafermion sequence (Laughlin, Moore-Read, or Read-Rezayi) of fractional quantum Hall states. We uniquely define these states through two generalized clustering conditions: they vanish when either a cluster of k+2 electrons is put together or when two clusters of k+1 electrons are formed at different positions. For Abelian fractional quantum Hall states (k=1), our construction reproduces the Jain quasielectron wave function and elucidates the difference between the Jain and Laughlin quasielectrons.We present model wave functions for quasielectron (as opposed to quasihole) excitations of the unitary Z_{k} parafermion sequence (Laughlin, Moore-Read, or Read-Rezayi) of fractional quantum Hall states. We uniquely define these states through two generalized clustering conditions: they vanish when either a cluster of k+2 electrons is put together or when two clusters of k+1 electrons are formed at different positions. For Abelian fractional quantum Hall states (k=1), our construction reproduces the Jain quasielectron wave function and elucidates the difference between the Jain and Laughlin quasielectrons.

arXiv:0810.2366Physical Review LettersFeb 10, 200985 citations

Non-Abelian Quantum Hall States—Exclusion Statistics, K-Matrices, and Duality

Eddy Ardonne, Peter Bouwknegt, Kareljan Schoutens

arXiv:cond-mat/0004084Journal of Statistical PhysicsFeb 1, 200119 citations

Scaling and non-Abelian signature in fractional quantum Hall quasiparticle tunneling amplitude

Zi-Xiang Hu, Ki H Lee, Edward H. Rezayi +2 more

We study the scaling behavior in the tunneling amplitude when quasiparticles tunnel along a straight path between the two edges of a fractional quantum Hall annulus. Such scaling behavior originates from the propagation and tunneling of charged quasielectrons and quasiholes in an effective field analysis. In the limit when the annulus deforms continuously into a quasi-one-dimensional (1D) ring, we conjecture the exact functional form of the tunneling amplitude for several cases, which reproduces the numerical results in finite systems exactly. The results for Abelian quasiparticle tunneling is consistent with the scaling analysis; this allows for the extraction of the conformal dimensions of the quasiparticles. We analyze the scaling behavior of both Abelian and non-Abelian quasiparticles in the Read–Rezayi -parafermion states. Interestingly, the non-Abelian quasiparticle tunneling amplitudes exhibit non-trivial k -dependent corrections to the scaling exponent.We study the scaling behavior in the tunneling amplitude when quasiparticles tunnel along a straight path between the two edges of a fractional quantum Hall annulus. Such scaling behavior originates from the propagation and tunneling of charged quasielectrons and quasiholes in an effective field analysis. In the limit when the annulus deforms continuously into a quasi-one-dimensional (1D) ring, we conjecture the exact functional form of the tunneling amplitude for several cases, which reproduces the numerical results in finite systems exactly. The results for Abelian quasiparticle tunneling is consistent with the scaling analysis; this allows for the extraction of the conformal dimensions of the quasiparticles. We analyze the scaling behavior of both Abelian and non-Abelian quasiparticles in the Read–Rezayi -parafermion states. Interestingly, the non-Abelian quasiparticle tunneling amplitudes exhibit non-trivial k -dependent corrections to the scaling exponent.

arXiv:1011.4716New Journal of PhysicsMar 23, 20117 citations

Quasielectrons in Abelian and non-Abelian Quantum Hall States

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Quasielectrons in Abelian and non-Abelian Quantum Hall States

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