Eddy Ardonne et al J. Stat. Mech. (2008) P04016 doi:10.1088/1742-5468/2008/04/P04016
Degeneracy of non-Abelian quantum Hall states on the torus: domain walls and conformal field theory
Eddy Ardonne1,2, Emil J Bergholtz3, Janik Kailasvuori4 and Emma Wikberg3
Show affiliationsWe 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 
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.
- Keywords
- PACS
- MSC
-
81V70 Many-body theory; quantum Hall effect
82B23 Exactly solvable models; Bethe ansatz
81T40 Two-dimensional field theories, conformal field theories, etc.
- Subjects
- Dates
-
Issue 04 (April 2008)
Received 13 February 2008, accepted for publication 19 March 2008
Published 14 April 2008
-
Degeneracy of non-Abelian quantum Hall states on the torus: domain walls and conformal field theory
Eddy Ardonne et al J. Stat. Mech. (2008) P04016
-
Large deviations of the free energy in diluted mean-field spin-glass
Giorgio Parisi and Tommaso Rizzo 2010 J. Phys. A: Math. Theor. 43 045001
-
An optimized kHz two-colour high harmonic source for seeding free-electron lasers and plasma-based soft x-ray lasers
G Lambert et al 2009 New J. Phys. 11 083033
-
Crystal growth, structure, and physical properties of Ln(Cu,Al)12 (Ln = Y, Ce, Pr, Sm, and Yb) and Ln(Cu,Ga)12 (Ln = Y, Gd–Er, and Yb)
Brenton L Drake et al 2010 J. Phys.: Condens. Matter 22 066001
-
Absolute angle-differential cross sections for electron-impact excitation of neon within the first 3.5 eV above threshold
M Allan et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 044009
-
Advanced spectroscopic synchrotron techniques to unravel the intrinsic properties of dilute magnetic oxides: the case of Co:ZnO
A Ney et al 2010 New J. Phys. 12 013020
-
Effective three-body interactions of neutral bosons in optical lattices
P R Johnson et al 2009 New J. Phys. 11 093022
-
Zooming in on local level statistics by supersymmetric extension of free probability
S Mandt and M R Zirnbauer 2010 J. Phys. A: Math. Theor. 43 025201
-
The matchmaking paradox: a statistical explanation
Iddo I Eliazar and Igor M Sokolov 2010 J. Phys. A: Math. Theor. 43 055001
-
On correlation functions of integrable models associated with the six-vertex R-matrix
N Kitanine et al J. Stat. Mech. (2007) P01022
Users also read
What's this?- Topological estimation of percolation thresholds
- Utilizing Minkowski functionals for image analysis: a marching square algorithm
- Spin chain description of rotating bosons at ν = 1
Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- The effective temperature
- Unconventional phase transitions in a constrained single polymer chain