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

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

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

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.Comment: LaTeX2e, 40 page

Non-Abelian spin-singlet quantum Hall states: wave functions and quasihole state counting

We investigate a class of non-Abelian spin-singlet (NASS) quantum Hall phases, proposed previously. The trial ground and quasihole excited states are exact eigenstates of certain k+1-body interaction Hamiltonians. The k=1 cases are the familiar Halperin Abelian spin-singlet states. We present closed-form expressions for the many-body wave functions of the ground states, which for k>1 were previously defined only in terms of correlators in specific conformal field theories. The states contain clusters of k electrons, each cluster having either all spins up, or all spins down. The ground states are non-degenerate, while the quasihole excitations over these states show characteristic degeneracies, which give rise to non-Abelian braid statistics. Using conformal field theory methods, we derive counting rules that determine the degeneracies in a spherical geometry. The results are checked against explicit numerical diagonalization studies for small numbers of particles on the sphere.Comment: 17 pages, 4 figures, RevTe

Realizing All so(N)1 Quantum Criticalities in Symmetry Protected Cluster Models

We show that all so(N)1 universality class quantum criticalities emerge when one-dimensional generalized cluster models are perturbed with Ising or Zeeman terms. Each critical point is described by a low-energy theory of N linearly dispersing fermions, whose spectrum we show to precisely match the prediction by so(N)1 conformal field theory. Furthermore, by an explicit construction we show that all the cluster models are dual to nonlocally coupled transverse field Ising chains, with the universality of the so(N)1 criticality manifesting itself as N of these chains becoming critical. This duality also reveals that the symmetry protection of cluster models arises from the underlying Ising symmetries and it enables the identification of local representations for the primary fields of the so(N)1 conformal field theories. For the simplest and experimentally most realistic case that corresponds to the original one-dimensional cluster model with local three-spin interactions, our results show that the su(2)2≃so(3)1 Wess-Zumino-Witten model can emerge in a local, translationally invariant, and Jordan-Wigner solvable spin-1/2 model

Separation of spin and charge in paired spin-singlet quantum Hall states

We propose a series of paired spin-singlet quantum Hall states, which exhibit a separation of spin and charge degrees of freedom. The fundamental excitations over these states, which have filling fraction \nu=2/(2m+1) with m an odd integer, are spinons (spin-1/2 and charge zero) or fractional holons (charge +/- 1/(2m+1) and spin zero). The braid statistics of these excitations are non-abelian. The mechanism for the separation of spin and charge in these states is topological: spin and charge excitations are liberated by binding to a vortex in a p-wave pairing condensate. We briefly discuss related, abelian spin-singlet states and possible transitions.Comment: 4 pages, uses revtex

The structure of spinful quantum Hall states: a squeezing perspective

We provide a set of rules to define several spinful quantum Hall model states. The method extends the one known for spin polarized states. It is achieved by specifying an undressed root partition, a squeezing procedure and rules to dress the configurations with spin. It applies to both the excitation-less state and the quasihole states. In particular, we show that the naive generalization where one preserves the spin information during the squeezing sequence, may fail. We give numerous examples such as the Halperin states, the non-abelian spin-singlet states or the spin-charge separated states. The squeezing procedure for the series (k=2,r) of spinless quantum Hall states, which vanish as r powers when k+1 particles coincide, is generalized to the spinful case. As an application of our method, we show that the counting observed in the particle entanglement spectrum of several spinful states matches the one obtained through the root partitions and our rules. This counting also matches the counting of quasihole states of the corresponding model Hamiltonians, when the latter is available.Comment: 19 pages, 7 figures; v2: minor changes, and added references. Mathematica packages are available for downloa

Fusion products, Kostka polynomials, and fermionic characters of su(r+1)_k

Using a form factor approach, we define and compute the character of the fusion product of rectangular representations of \hat{su}(r+1). This character decomposes into a sum of characters of irreducible representations, but with q-dependent coefficients. We identify these coefficients as (generalized) Kostka polynomials. Using this result, we obtain a formula for the characters of arbitrary integrable highest-weight representations of \hat{su}(r+1) in terms of the fermionic characters of the rectangular highest weight representations.Comment: 21 pages; minor changes, typos correcte