Parafermion statistics and the application to non-abelian quantum Hall states

The (exclusion) statistics of parafermions is used to study degeneracies of quasiholes over the paired (or in general clustered) quantum Hall states. Focus is on the Z_k and su(3)_k/u(1)^2 parafermions, which are used in the description of spin-polarized and spin-singled clustered quantum Hall states.Comment: 15 pages, minor changes, as publishe

Domain walls, fusion rules and conformal field theory in the quantum Hall regime

We provide a simple way to obtain the fusion rules associated with elementary quasi-holes over quantum Hall wave functions, in terms of domain walls. The knowledge of the fusion rules is helpful in the identification of the underlying conformal field theory describing the wave functions. We obtain the fusion rules, and explicitly give a conformal field theory description, for a two-parameter family (k,r) of wave functions. These include the Laughlin, Moore-Read and Read-Rezayi states when r=2. The `gaffnian' wave function is the prototypical example for r>2, in which case the conformal field theory is non-unitary.Comment: 4 page

Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry

We show that a large class of bosonic spin-singlet Fractional Quantum Hall model wave-functions and their quasi-hole excitations can be written in terms of Jack polynomials with a prescribed symmetry. Our approach describes new spin-singlet quantum Hall states at filling fraction nu = 2k/(2r-1) and generalizes the (k,r) spin-polarized Jack polynomial states. The NASS and Halperin spin singlet states emerge as specific cases of our construction. The polynomials express many-body states which contain configurations obtained from a root partition through a generalized squeezing procedure involving spin and orbital degrees of freedom. The corresponding generalized Pauli principle for root partitions is obtained, allowing for counting of the quasihole states. We also extract the central charge and quasihole scaling dimension, and propose a conjecture for the underlying CFT of the (k, r) spin-singlet Jack states.Comment: 17 pages, 1 figur

Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas

We give a complete description of the graded multiplicity space which appears in the Feigin-Loktev fusion product [FL99] of graded Kirillov-Reshetikhin modules for all simple Lie algebras. This construction is used to obtain an upper bound formula for the fusion coefficients in these cases. The formula generalizes the case of g=A_r [AKS06], where the multiplicities are generalized Kostka polynomials [SW99,KS02]. In the case of other Lie algebras, the formula is the the fermionic side of the X=M conjecture [HKO+99]. In the cases where the Kirillov-Reshetikhin conjecture, regarding the decomposition formula for tensor products of KR-modules, has been been proven in its original, restricted form, our result provides a proof of the conjectures of Feigin and Loktev regarding the fusion product multiplicites.Comment: 22 pages; v2: minor changes; v3: exposition clarifie

Non-Abelian statistics in the interference noise of the Moore-Read quantum Hall state

We propose noise oscillation measurements in a double point contact, accessible with current technology, to seek for a signature of the non-abelian nature of the \nu=5/2 quantum Hall state. Calculating the voltage and temperature dependence of the current and noise oscillations, we predict the non-abelian nature to materialize through a multiplicity of the possible outcomes: two qualitatively different frequency dependences of the nonzero interference noise. Comparison between our predictions for the Moore-Read state with experiments on \nu=5/2 will serve as a much needed test for the nature of the \nu=5/2 quantum Hall state.Comment: 4 pages, 4 figures v2: typo's corrected, discussions clarified, references adde