Mutual statistics, braid group, and the fractional quantum Hall effect

We show that the notion of mutual statistics arises naturally from the representation theory of the braid group over the multi-sheeted surface. A Hamiltonian which describes particles moving on the double-sheeted surface is proposed as a model for the bilayered fractional quantum Hall effect (FQHE) discovered recently. We explicitly show that the quasi-holes of the bilayered Hall fluid display fractional mutual statistics. A model for 3-dimensional FQHE using the multi-layered sample is suggested.Comment: LaTex 26 page

Proposed Detection of Time Reversal Symmetry in Topological Surface States

By employing T-matrix approach, we investigate a nonmagnetic impurity located on the surface of three-dimensional topological insulators, where the time reversal symmetry is preserved. It is shown that the images of the local density of states (LDOS) around the single impurity have the dip-hump structures with six-fold symmetry at different bias voltages. The peaks are produced by quasiparticle interference while the local minima at the backscattering wave vectors are due to the absence of backscatterings. With increasing the bias voltage, the peaks and dips move forward to the location of the impurity. These dips at the backscattering wave vectors in the LDOS spectra can be regarded as a signature of the time reversal symmetry in the topological surface states, which could be observed by scanning tunneling microscopy.Comment: 4 pages, 4 figure

States of Local Moment Induced by Nonmagnetic Impurities in Cuprate Superconductors

By using a model Hamiltonian with d-wave superconductivity and competing antiferromagnetic (AF) orders, the local staggered magnetization distribution due to nonmagnetic impurities in cuprate superconductors is investigated. From this, the net magnetic moment induced by a single or double impurities can be obtained. We show that the net moment induced by a single impurity corresponds to a local spin with S_z=0, or 1/2 depending on the strength of the AF interaction and the impurity scattering. When two impurities are placed at the nearest neighboring sites, the net moment is always zero. For two unitary impurities at the next nearest neighboring sites, and at sites separated by a Cu-ion site, the induced net moment has S_z=0, or 1/2, or 1. The consequence of these results on experiments will be discussed.Comment: 4 pages, 4 figure

Derivative Computations and Robust Standard Errors for Linear Mixed Effects Models in lme4

While robust standard errors and related facilities are available in R for many types of statistical models, the facilities are notably lacking for models estimated via lme4. This is because the necessary statistical output, including the Hessian and casewise gradient of random effect parameters, is not immediately available from lme4 and is not trivial to obtain. In this article, we supply and describe two new functions to obtain this output from Gaussian mixed models: estfun.lmerMod() and vcov.full.lmerMod(). We discuss the theoretical results implemented in the code, focusing on calculation of robust standard errors via package sandwich. We also use the Sleepstudy data to illustrate the code and compare it to a benchmark from package lavaan.Comment: Accepted at Journal of Statistical Softwar

Absence of broken inversion symmetry phase of electrons in bilayer graphene under charge density fluctuations

On a lattice model, we study the possibility of existence of gapped broken inversion symmetry phase (GBISP) of electrons with long-range Coulomb interaction in bilayer graphene using both self-consistent Hartree-Fock approximation (SCHFA) and the renormalized-ring-diagram approximation (RRDA). RRDA takes into account the charge-density fluctuations beyond the mean field. While GBISP at low temperature and low carrier concentration is predicted by SCHFA, we show here the state can be destroyed by the charge-density fluctuations. We also present a numerical algorithm for calculating the self-energy of electrons with the singular long-range Coulomb interaction on the lattice model.Comment: 8 pages, 6 figure