[en] We introduce a large N version of the spin quantum Hall transition problem. It is formulated as a problem of Dirac fermions coupled to disorder, whose Hamiltonian belong to the symmetry class C. The fermions carry spin degrees of freedom valued in the algebra sp(2N), the spin quantum Hall effect corresponding to N=1. Arguments based on renormalization group transformations as well as on a sigma model formulation, valid in the large N limit, indicate the existence of a crossover as N varies. Contrary to the N=1 case, the large N models are shown to lead to localized states at zero energy. We also present a sigma model analysis for the system of Dirac fermions coupled to only sp(2N) random gauge potentials, which reproduces known exact results

[en] Using a Lax pair based on twisted affine sl(2,R) Kac-Moody and Virasoro algebras, we deduce a r-matrix formulation of two dimensional reduced vacuum Einstein's equations. Whereas the fundamental Poisson brackets are non-ultralocal, they lead to pure c-number modified Yang-Baxter equations. We also describe how to obtain classical observables by imposing reasonable boundaries conditions. (author)

[en] We study the quantum Hall states that appear in the dilute limit of rotating ultracold fermionic gases when a single hyperfine species is present. We show that the p-wave scattering translates into a pure hard-core interaction in the lowest Landau level. The Laughlin wave function is then the exact ground state at filling fraction ν=1/3. We give estimates of some of the gaps of the incompressible liquids for ν=p/(2p±1). We estimate the mass of the composite fermions at ν=1/2. The width of the quantum Hall plateaus is discussed by considering the equation of state of the system

[en] We study the quantum Hall phases that appear in the dilute limit of rotating Bose-Einstein condensates. By exact diagonalization in a spherical geometry we obtain the ground state and low-lying excited states of a small number of bosons as a function of the filling fraction ν, the ratio of the number of bosons to the number of vortices. We show the occurrence of the Jain principal sequence of incompressible liquids for ν=2/3,3/4,4/3,5/4 in addition to the Laughlin state ν=1/2 as well as the Pfaffian state for ν=1. We give gap estimates by finite-size scaling of both charged and neutral excitations

[en] The Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) is a massive imaging survey, conducted between 2003 and 2008, with the MegaCam instrument, mounted on the CFHT-3.6-m telescope. With a 1 degree wide focal plane, made of 36 2048 × 4612 sensors totalling 340 megapixels, MegaCam was at the time the largest imager on the sky. The Supernova Legacy Survey (SNLS) uses the cadenced observations of the 4 deg"2 wide 'DEEP' layer of the CFHTLS to search and follow-up Type Ia supernovae (SNe Ia) and study the acceleration of the cosmic expansion. The reduction and calibration of the CFHTLS/SNLS datasets has posed a series of challenges. In what follows, we give a brief account of the photometric calibration work that has been performed on the SNLS data over the last decade

[en] We investigate some properties of the parafermionic states, which may occur in rapidly rotating ultracold bosonic atomic gases at lowest Landau level filling factor ν=k/2 (with k integer ≥2). These states have manifolds of quasihole states, which are expected to display non-Abelian statistics. We use exact diagonalizations in the spherical geometry to investigate the quasihole manifolds for quantum Hall states at ν=1, 3/2, 2, and 5/2. We show that there is a perfect agreement between numerical findings and the prediction of conformal field theory concerning the number of orbital angular momentum multiplets as a function of added vorticity. The overlap between quasihole candidate wave functions and the corresponding states for realistic delta function interactions between bosons is computed. This allows us to discuss the possible relevance of non-Abelian degeneracy in the physical situation of ultracold atoms

[en] We deduce a new set of symmetries and relations between the coefficients of the expansion of Abelian and non-Abelian fractional quantum Hall (FQH) states in free (bosonic or fermionic) many-body states. Our rules allow us to build an approximation of a FQH model state with an overlap increasing with growing system size (that may sometimes reach unity) while using a fraction of the original Hilbert space. We prove these symmetries by deriving a previously unknown recursion formula for all the coefficients of the Slater expansion of the Laughlin, Read-Rezayi, and many other states (all Jacks multiplied by Vandermonde determinants), which completely removes the current need for diagonalization procedures for these model Hamiltonians.

[en] We investigated the non-universal part of the orbital entanglement spectrum (OES) of the ν = 1/3 fractional quantum Hall (FQH) effect ground state using Coulomb interactions. The non-universal part of the spectrum is the part that is missing in the Laughlin model state OES, whose level counting is completely determined by its topological order. We found that the OES levels of the Coulomb interaction ground state are organized in a hierarchical structure that mimics the excitation-energy structure of the model pseudopotential Hamiltonian, which has a Laughlin ground state. These structures can be accurately modeled using Jain's 'composite fermion' quasihole-quasiparticle excitation wave functions. To emphasize the connection between the entanglement spectrum and the energy spectrum, we also considered the thermodynamical OES of the model pseudopotential Hamiltonian at the finite temperature. The good match observed between the thermodynamical OES and the Coulomb OES suggests that there is a relation between the entanglement gap and the true energy gap. (paper)

[en] We obtain several clustering properties of the Jain states at filling (k/2k+1): they are a product of a Vandermonde determinant and a bosonic polynomial at filling (k/k+1) which vanishes when k+1 particles cluster together. We show that all Jain states satisfy a 'squeezing rule' which severely reduces the dimension of the Hilbert space necessary to generate them. We compute the topological entanglement spectrum of the Jain ν=(2/5) state and compare it to both the Coulomb ground state and the nonunitary Gaffnian state. All three states have a very similar 'low-energy' structure. However, the Jain state entanglement 'edge' state counting matches both the Coulomb counting as well as two decoupled U(1) free bosons, whereas the Gaffnian edge counting misses some of the edge states of the Coulomb spectrum.

[en] We study the fractional quantum Hall effect in a bilayer with charge-distribution imbalance induced, for instance, by a bias gate voltage. The bilayer can either be intrinsic or it can be formed spontaneously in wide quantum wells, due to the Coulomb repulsion between electrons. We focus on fractional quantum Hall effect in asymmetric bilayer systems at filling factor ν = 4/11 and show that an asymmetric Halperin-like trial wavefunction gives a valid description of the ground state of the system