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Certain fractional quantum Hall wavefunctions -- particularly including the Laughlin, Moore-Read, and Read-Rezayi wavefunctions -- have special structure that makes them amenable to analysis using an exeptionally wide range of techniques…
Partition functions of edge excitations are obtained for non-Abelian Hall states in the second Landau level, such as the anti-Read-Rezayi state, the Bonderson-Slingerland hierarchy and the Wen non-Abelian fluid, as well as for the…
We construct effective $\mathrm{U}(2)$ Chern-Simons-Ginzburg-Landau theories for Abelian and non-Abelian fractional quantum Hall hierarchies for those which had previously been described only through categorical data or trial wavefunctions.…
Strong interaction between electrons in two-dimensional systems in the presence of a high magnetic field gives rise to fractional quantum Hall states that host quasiparticles with fractional charge and fractional exchange statistics. Here,…
The observed fractional quantum Hall (FQH) plateaus follow a recurring hierarchical structure that allows an understanding of complex states based on simpler ones. Condensing the elementary quasiparticles of an Abelian FQH state results in…
Quasihole excitations in fractional quantum Hall (FQH) systems exhibit fractional statistics and fractional spin, but how the spin-statistics relation emerges from many-body physics remains poorly understood. Here we prove a spin-statistics…
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…
We formulate a theory of non-Abelian fractional quantum Hall states by considering an anisotropic system consisting of coupled, interacting one dimensional wires. We show that Abelian bosonization provides a simple framework for…
Explicit wave functions for the hierarchy of fractionally quantized Hall states are proposed, and a method for integrating out the quasiparticle coordinates in the spherical geometry is developed. Their energies and overlaps with the exact…
The quasiparticle propagator of Haldane-Rezayi(HR) fractional quantum Hall (FQH) state is calculated, based on a chiral fermion model (or a Weyl fermion model) equipped with a hidden spin SU(2) symmetry. The spectrum of the chiral fermion…
We compute the physical properties of non-Abelian Fractional Quantum Hall (FQH) states described by Jack polynomials at general filling $\nu=\frac{k}{r}$. For $r=2$, these states are identical to the $Z_k$ Read-Rezayi parafermions, whereas…
We consider the quasihole wavefunctions of the non-abelian Read-Rezayi quantum Hall states which are given by the conformal blocks of the minimal model WA_{k-1}(k+1,k+2) of the WA_{k-1} algebra. By studying the degenerate representations of…
It has been shown that different Abelian and non-Abelian fraction quantum Hall states can be characterized by patterns of zeros described by sequences of integers {S_a}. In this paper, we will show how to use the data {S_a} to calculate…
We derive the braid relations of the charged anyons interacting with a magnetic field on Riemann surfaces. The braid relations are used to calculate the quasiparticle's spin in the fractional quantum Hall states on Riemann surfaces. The…
In groups with involution a nonassociative product of elements is defined, which leads to the definition of a certain type of quasigroups. These quasigroups are represented by square tables of complex numbers, with inverses, which differ…
It is shown, with the help of exact diagonalization studies on systems with up to sixteen electrons, in the presence of up to two delta function impurities, that the Pfaffian model is inadequate for the actual quasiholes and quasiparticles…
Quasiparticle spin (in the spacetime sense) couples to curvature of space. Here this fact is used to calculate the spin of quasiholes in trial quantum Hall states by adiabatically dragging them around on a sphere, for trial states given by…
Cumrun Vafa proposed a new unifying model for the principal series of FQHE which predicts non-Abelian statistics of the quasi-holes. The many-body Hamiltonian supporting these topological phases of matter is invariant under four…
The possibility of realizing bosonic fractional quantum Hall effect in ultra-cold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and…
I propose that non-Abelian topological order can emerge from the organization of quantum particles into identical indistinguishable copies of the same quantum many-body state. Quantum indistinguishability (symmetrization) of the…