arXiv subjects
Publications and source records attributed to K. Schoutens.
We briefly summarize properties of quantum Hall states with a pairing or clustering property. Their study employs a fundamental connection with parafermionic Conformal Field Theories. We report on closed form expressions for the many-body wave functions and on multiplicities of the fundamental quasi-hole excitations.
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.
The non-Fermi liquid physics at the edge of fractional quantum Hall systems is described by specific chiral Conformal Field Theories with central charge c=1. The charged quasi-particles in these theories have fractional charge and obey a form of fractional statistics. In this paper we study form factors, which are matrix elements of physical (conformal) operators, evaluated in a quasi-particle basis that is organized according to the rules of fractional exclusion statistics. Using the systematics of Jack polynomials, we derive selection rules for a special class of form factors. We argue that finite temperature Green's functions can be evaluated via systematic form factor expansions, using form factors such as those computed in this paper and thermodynamic distribution functions for fractional exclusion statistics. We present a specific case study where we demonstrate that the form factor expansion shows a rapid convergence.
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.
Two fundamental aspects of so-called non-abelian quantum Hall states (the q-pfaffian states and more general) are a (generalized) pairing of the participating electrons and the non-abelian statistics of the quasi-hole excitations. In this paper, we show that these two aspects are linked by a duality relation, which can be made manifest by considering the K-matrices that describe the exclusion statistics of the fundamental excitations in these systems.
I comment on the paper hep-th/9808013 by A. Berkovich and B.M. McCoy.
We present a new class of non-abelian spin-singlet quantum Hall states, generalizing Halperin's abelian spin-singlet states and the Read-Rezayi non-abelian quantum Hall states for spin-polarized electrons. We label the states by (k,M) with M odd (even) for fermionic (bosonic) states, and find a filling fraction $ν=2k/(2kM+3)$. The states with M=0 are bosonic spin-singlet states characterized by an SU(3)_k symmetry. We explain how an effective Landau-Ginzburg theory for the SU(3)_2 state can be constructed. In general, the quasi-particles over these new quantum Hall states carry spin, fractional charge and non-abelian quantum statistics.
We discuss a quasi-particle formulation of effective edge theories for the fractional quantum Hall effect. Fundamental quasi-particles for the Laughlin state with filling fraction ν=1/3 are edge electrons of charge -e and edge quasi-holes of charge +e/3. These quasi-particles satisfy exclusion statistics in the sense of Haldane. We exploit algebraic properties of edge electrons to derive a kinetic equation for charge transport between a ν=1/3 fractional quantum Hall edge and a normal metal.
We systematically study the exclusion statistics for quasi-particles for Conformal Field Theory spectra by employing a method based on recursion relations for truncated spectra. Our examples include generalized fermions in c<1 unitary minimal models, Z_k parafermions, and spinons for the su(n)_1, so(n)_1 and sp(2n)_1 Wess-Zumino-Witten models. For some of the latter examples we present explicit expressions for finitized affine characters and for the N-spinon decomposition of affine characters.
We propose a quasi-particle formulation of effective edge theories for the fractional quantum Hall effect. For the edge of a Laughlin state with filling fraction ν=1/m, our fundamental quasi-particles are edge electrons of charge -e and edge quasi-holes of charge +e/m. These quasi-particles satisfy exclusion statistics in the sense of Haldane. We exploit algebraic properties of edge electrons to derive a kinetic equation for charge transport between a ν=1/m fractional quantum Hall edge and a normal metal. We also analyze alternative `Boltzmann' equations that are directly based on the exclusion statistics properties of edge quasi-particles. Generalizations to more general filling fractions (Jain series) are briefly discussed.
We determine the exclusion statistics properties of the fundamental edge quasi-particles over a specific $ν=\half$ non-abelian quantum Hall state known as the pfaffian. The fundamental excitations are the edge electrons of charge $-e$ and the edge quasi-holes of charge $+{e \over 4}$. We explicitly determine thermodynamic distribution functions and establish a duality which generalizes the duality for fractional exclusion statistics in the sense of Haldane.
We analyze critical and massive SO(5) superspin regimes for correlated electrons on a two-chain ladder. We identify fundamental low energy excitations, which carry the quantum numbers of a free electron, and can be probed in (inverse) photo-emission experiments. These excitations do not obey the usual Pauli Principle, but are governed by specific forms of so-called non-abelian exclusion statistics.
We propose a new method for investigating the exclusion statistics of quasi-particles in Conformal Field Theory (CFT) spectra. The method leads to one-particle distribution functions, which generalize the Fermi-Dirac distribution. For the simplest $su(n)$ invariant CFTs we find a generalization of Gentile parafermions, and we obtain new distributions for the simplest $Z_N$-invariant CFTs. In special examples, our approach reproduces distributions based on `fractional exclusion statistics' in the sense of Haldane. We comment on applications to fractional quantum Hall effect edge theories.
We briefly review the general structure of integrable particle theories in 1+1 dimensions having N=1 supersymmetry. Examples are specific perturbed superconformal field theories (of Yang-Lee type) and the N=1 supersymmetric sine-Gordon theory. We comment on the modifications that are required when the N=1 supersymmetry algebra contains non-trivial topological charges.
We address two fundamental issues in the physics of the quantum Hall effect: a unified description of scaling behavior of conductances in the integral and fractional regimes, and a quasi-particle formulation of the chiral Luttinger Liquids that describe the dynamics of edge excitations in the fractional regime.
We present a `spinon formulation' of the $SU(n)_1$ Wess-Zumino-Witten models. Central to this approach are a set of massless quasi-particles, called `spinons', which transform in the representation ${\bf \bar{n}}$ of $su(n)$ and carry fractional statistics of angle $θ= π/n$. Multi-spinon states are grouped into irreducible representations of the yangian $Y(sl_n)$. We give explicit results for the $su(n)$ content of these yangian representations and present $N$-spinon cuts of the WZW character formulas. As a by-product, we obtain closed expressions for characters of the $su(n)$ Haldane-Shastry spin chains.
We study two-dimensional integrable $N=1$ supersymmetric theories (without topological charges) in the presence of a boundary. We find a universal ratio between the reflection amplitudes for particles that are related by supersymmetry and we propose exact reflection matrices for the supersymmetric extensions of the multi-component Yang-Lee models and for the breather multiplets of the supersymmetric sine-Gordon theory. We point out the connection between our reflection matrices and the classical boundary actions for the supersymmetric sine-Gordon theory as constructed by Inami, Odake and Zhang \cite{IOZ}.
We briefly review results on two-dimensional supersymmetric quantum field theories that exhibit factorizable particle scattering. Our particular focus is on a series of $N\!=\!1$ supersymmetric theories, for which exact $S$-matrices have been obtained. A Thermodynamic Bethe Ansatz (TBA) analysis for these theories has confirmed the validity of the proposed $S$-matrices and has pointed at an interesting `folding' relation with a series of $N\!=\!2$ supersymmetric theories.