Non-abelian quantum Hall states - exclusion statistics, K-matrices and duality

Abstract

We study excitations in edge theories for non-abelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edge-electrons and edge-quasiholes, we arrive at a novel K-matrix structure. Interestingly, the duality between the electron and quasihole sectors links the pseudoparticles that are characteristic for non-abelian statistics with composite particles that are associated to the `pairing physics' of the non-abelian quantum Hall states.

LaTeX2e, 40 pages

References in corpus (15)

• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=5/2 Landau Level Filling Factor
• A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
• New Class of Non-Abelian Spin-Singlet Quantum Hall States
• Character Formulae of ${\widehat{sl}}_n$-Modules and Inhomogeneous Paths
• Exclusion Statistics in Conformal Field Theory -- generalized fermions and spinons for level-1 WZW theories
• (Mis-)handling gauge invariance in the theory of the quantum Hall effect III: The instanton vacuum and chiral edge physics
• Quasi-particles in Fractional Quantum Hall Effect Edge Theories
• Parafermion Statistics and Quasihole Excitations for the Generalizations of the Paired Quantum Hall States
• Exclusion statistics for non-abelian quantum Hall states
• Non-abelian Exclusion Statistics
• Spinon statistics in integrable spin-S Heisenberg chains
• K-matrices for non-abelian quantum Hall states
• Exclusion statistics in conformal field theory and the UCPF for WZW models
• q-Identities and affinized projective varieties, II. Flag varieties

Cited by in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons and the quantum Hall effect - a pedagogical review
• Non-Abelian spin-singlet quantum Hall states: wave functions and quasihole state counting
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Separation of spin and charge in paired spin-singlet quantum Hall states
• The structure of spinful quantum Hall states: a squeezing perspective
• Filling the Bose sea: symmetric quantum Hall edge states and affine characters
• Parafermion statistics and the application to non-abelian quantum Hall states
• Fermionic characters of arbitrary highest-weight integrable sl_{r+1}-modules
• Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions
• K-matrices for 2D conformal field theories
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet