Universality of the edge tunneling exponent of fractional quantum Hall liquids

Recent calculations of the edge tunneling exponents in quantum Hall states appear to contradict their topological nature. We revisit this issue and find no fundamental discrepancies. In a microscopic model of fractional quantum Hall liquids with electron-electron interaction and confinement, we calculate the edge Green's function via exact diagonalization. Our results for $\nu = 1/3$ and 2/3 suggest that in the presence of Coulomb interaction, the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, are the parameters that are relevant to the universality of the electron tunneling I-V exponent.Comment: 5 pages, 3 figure

Generalized Quantum Hall Projection Hamiltonians

Certain well known quantum Hall states -- including the Laughlin states, the Moore-Read Pfaffian, and the Read-Rezayi Parafermion states -- can be defined as the unique lowest degree symmetric analytic function that vanishes as at least p powers as some number (g+1) of particles approach the same point. Analogously, these same quantum Hall states can be generated as the exact highest density zero energy state of simple angular momentum projection operators. Following this theme we determine the highest density zero energy state for many other values of p and g.Comment: 9 page

Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement

We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at filling fraction $\nu = 5/2$, with Coulomb interaction and background confining potential. We find the Moore-Read ground state is stable within a finite but narrow window in parameter space. The corresponding low-energy excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge $+e/4$ quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for Majorana fermions, clearly indicating the non-Abelian nature of the quasihole.Comment: 4 pages, 3 figures. New version shortened for PRL. Corrected typo

Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level

We present results of extensive numerical calculations on the ground state of electrons in the first excited (n=1) Landau level with Coulomb interactions, and including non-zero thickness effects, for filling factors 12/5 and 13/5 in the torus geometry. In a region that includes these experimentally-relevant values, we find that the energy spectrum and the overlaps with the trial states support the previous hypothesis that the system is in the non-Abelian k = 3 liquid phase we introduced in a previous paper.Comment: 5 pages (Revtex4), 7 figure

Coulomb and Hard Core Skyrmion Tails

Quantum Hall skyrmions are quantized solitons of a ferromagnetic O(3) sigma-model. The reference, classical, solutions depend upon the interaction between the electrons and exhibit completely different asymptotic profiles for the physical Coulomb interaction than for the model hard core interaction frequently used to generate variational wavefunctions. In this note we show, by means of numerical calculations on (large) finite size systems at nu=1, that this physically important difference, crucial for a sharp definition of their statistics, persists for the quantized skyrmions at n=1.Comment: Revtex 9 pages, figs.ps files at ftp://landau.calstatela.edu/pub/tailfig

A nu=2/5 Paired Wavefunction

We construct a wavefunction, generalizing the well known Moore-Read Pfaffian, that describes spinless electrons at filling fraction nu=2/5 (or bosons at filling fraction nu=2/3) as the ground state of a very simple three body potential. We find, analogous to the Pfaffian, that when quasiholes are added there is a ground state degeneracy which can be identified as zero-modes of the quasiholes. The zero-modes are identified as having semionic statistics. We write this wavefunction as a correlator of the Virasoro minimal model conformal field theory M(5,3). Since this model is non-unitary, we conclude that this wavefunction is a quantum critical state. Nonetheless, we find that the overlaps of this wavefunction with exact diagonalizations in the lowest and first excited Landau level are very high, suggesting that this wavefunction may have experimental relevance for some transition that may occur in that regime.Comment: 13 pages, 2 figure

Low ordered magnetic moment by off-diagonal frustration in undoped parent compounds to iron-based high-Tc superconductors

A Heisenberg model over the square lattice recently introduced by Si and Abrahams to describe local-moment magnetism in the new class of Fe-As high-Tc superconductors is analyzed in the classical limit and on a small cluster by exact diagonalization. In the case of spin-1 iron atoms, large enough Heisenberg exchange interactions between neighboring spin-1/2 moments on different iron 3d orbitals that frustrate true magnetic order lead to hidden magnetic order that violates Hund's rule. It accounts for the low ordered magnetic moment observed by elastic neutron diffraction in an undoped parent compound to Fe-As superconductors. We predict that low-energy spin-wave excitations exist at wavenumbers corresponding to either hidden Neel or hidden ferromagnetic order.Comment: 7 pages, 6 figures, version published in Physical Review Letter