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

Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States

We develop the Density Matrix Renormalization Group (DMRG) technique for numerically studying incompressible fractional quantum Hall (FQH) states on the sphere. We calculate accurate estimates for ground state energies and excitationgaps at FQH filling fractions \nu=1/3 and \nu=5/2 for systems that are almost twice as large as the largest ever studied by exact diagonalization. We establish, by carefully comparing with existing numerical results on smaller systems, that DMRG is a highly effective numerical tool for studying incompressible FQH states.Comment: 5 pages, 4 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

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

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

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