Fractional statistics in the fractional quantum Hall effect

A microscopic confirmation of the fractional statistics of the {\em quasiparticles} in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at $\nu=1/3$ and $\nu=2/5$ by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the statistics. The conditions for the applicability of the fractional statistics concept are discussed.Comment: Phys. Rev. Lett., in pres

Logarithmic temperature dependence of conductivity at half-integer filling factors: Evidence for interaction between composite fermions

We have studied the temperature dependence of diagonal conductivity in high-mobility two-dimensional samples at filling factors $\nu=1/2$ and 3/2 at low temperatures. We observe a logarithmic dependence on temperature, from our lowest temperature of 13 mK up to 400 mK. We attribute the logarithmic correction to the effects of interaction between composite fermions, analogous to the Altshuler-Aronov type correction for electrons at zero magnetic field. The paper is accepted for publication in Physical Review B, Rapid Communications.Comment: uses revtex macro

Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness

The activation gaps for fractional quantum Hall states at filling fractions $\nu=n/(2n+1)$ are computed for heterojunction, square quantum well, as well as parabolic quantum well geometries, using an interaction potential calculated from a self-consistent electronic structure calculation in the local density approximation. The finite thickness is estimated to make $\sim$30% correction to the gap in the heterojunction geometry for typical parameters, which accounts for roughly half of the discrepancy between the experiment and theoretical gaps computed for a pure two dimensional system. Certain model interactions are also considered. It is found that the activation energies behave qualitatively differently depending on whether the interaction is of longer or shorter range than the Coulomb interaction; there are indications that fractional Hall states close to the Fermi sea are destabilized for the latter.Comment: 32 pages, 13 figure

One-Dimensional Theory of the Quantum Hall System

We consider the lowest Landau level on a torus as a function of its circumference $L_1$. When $L_1\to 0$, the ground state at general rational filling fraction is a crystal with a gap--a Tao-Thouless state. For filling fractions $\nu=p/(2pm+1)$, these states are the limits of Laughlin's or Jain's wave functions describing the gapped quantum Hall states when $L_1\to \infty$. For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral dipoles, or rather to a Luttinger liquid modification thereof, at $L_1\sim5$ magnetic lengths. This state is a version of the Rezayi-Read state, and develops continuously into the state that is believed to describe the observed metallic phase as $L_1\to \infty$. Furthermore, the effective Landau level structure that emerges within the lowest Landau level follows from the magnetic symmetries.Comment: 4 pages, 1 figur

Lorentz shear modulus of a two-dimensional electron gas at high magnetic field

We show that the Lorentz shear modulus -- one of the three elastic moduli of a homogeneous electron gas in a magnetic field -- can be calculated exactly in the limit of high magnetic field (i.e. in the lowest Landau level). Its value is $\pm \hbar n/4$, where $n$ is the two-dimensional electron density and the sign is determined by the orientation of the magnetic field. We use this result to refine our previous calculations of the dispersion of the collective modes of fractional quantum Hall liquids.Comment: 4 pages, 1 figur

Spin Transition in the Half-Filled Landau Level

The transition from partial to complete spin polarization of two-dimensional electrons at half filling of the lowest Landau level has been studied using resistively-detected nuclear magnetic resonance (RDNMR). The nuclear spin-lattice relaxation time is observed to be density independent in the partially polarized phase but to increase sharply at the transition to full polarization. At low temperatures the RDNMR signal exhibits a strong maximum near the critical density.Comment: 4 pages, 3 postscript figures. As published in Phys. Rev. Lett. 98, 086801 (2007

Likelihood Analysis of Cosmic Shear on Simulated and VIRMOS-DESCART Data

We present a maximum likelihood analysis of cosmological parameters from measurements of the aperture mass up to 35 arcmin, using simulated and real cosmic shear data. A four-dimensional parameter space is explored which examines the mean density \Omega_M, the mass power spectrum normalization \sigma_8, the shape parameter \Gamma and the redshift of the sources z_s. Constraints on \Omega_M and \sigma_8 (resp. \Gamma and z_s) are then given by marginalizing over \Gamma and z_s (resp. \Omega_M and \sigma_8). For a flat LCDM cosmologies, using a photometric redshift prior for the sources and \Gamma \in [0.1,0.4], we find \sigma_8=(0.57\pm0.04) \Omega_M^{(0.24\mp 0.18) \Omega_M-0.49} at the 68% confidence level (the error budget includes statistical noise, full cosmic variance and residual systematic). The estimate of \Gamma, marginalized over \Omega_M \in [0.1,0.4], \sigma_8 \in [0.7,1.3] and z_s constrained by photometric redshifts, gives \Gamma=0.25\pm 0.13 at 68% confidence. Adopting h=0.7, a flat universe, \Gamma=0.2 and \Omega_m=0.3 we find \sigma_8=0.98 \pm0.06 . Combined with CMB, our results suggest a non-zero cosmological constant and provide tight constraints on \Omega_M and \sigma_8. We finaly compare our results to the cluster abundance ones, and discuss the possible discrepancy with the latest determinations of the cluster method. In particular we point out the actual limitations of the mass power spectrum prediction in the non-linear regime, and the importance for its improvement.Comment: 11 pages, submitted to A&

Half-Integral Spin-Singlet Quantum Hall Effect

We provide numerical evidence that the ground state of a short range interaction model at $\nu=1/2$ is incompressible and spin-singlet for a wide range of repulsive interactions. Furthermore it is accurately described by a trial wave function studied earlier. For the Coulomb interaction we find that this wave function provides a good description of the lowest lying spin-singlet state, and propose that fractional quantum Hall effect would occur at $\nu=1/2$ if this state became the global ground state.Comment: Latex 13 pages, 3 figures upon reques

Two-photon exchange in elastic electron-nucleon scattering

A detailed study of two-photon exchange in unpolarized and polarized elastic electron--nucleon scattering is presented, taking particular account of nucleon finite size effects. Contributions from nucleon elastic intermediate states are found to have a strong angular dependence, which leads to a partial resolution of the discrepancy between the Rosenbluth and polarization transfer measurements of the proton electric to magnetic form factor ratio, G_E/G_M. The two-photon exchange contribution to the longitudinal polarization transfer P_L is small, whereas the contribution to the transverse polarization transfer P_T is enhanced at backward angles by several percent, increasing with Q^2. This gives rise to a small, ~3% suppression of G_E/G_M obtained from the polarization transfer ratio P_T/P_L at large Q^2. We also compare the two-photon exchange effects with data on the ratio of e^+ p to e^- p cross sections, which is predicted to be enhanced at backward angles. Finally, we evaluate the corrections to the form factors of the neutron, and estimate the elastic intermediate state contribution to the ^3He form factors

Emulating Non-Abelian Topological Matter in Cold Atom Optical Lattices

Certain proposed extended Bose-Hubbard models may exhibit topologically ordered ground states with excitations obeying non-Abelian braid statistics. A sufficient tuning of Hubbard parameters could yield excitation braiding rules allowing implementation of a universal set of topologically protected quantum gates. We discuss potential difficulties in realizing a model with a proposed non-Abelian topologically ordered ground state using optical lattices containing bosonic dipoles. Our direct implementation scheme does not realize the necessary anisotropic hopping, anisotropic interactions, and low temperatures