A Nearby Supernovae Search: Eros2

Type Ia supernovae (SNIa) have been used as approximate standard candles to measure cosmological parameters such as the Hubble constant and the deceleration parameter. These measurements rely on empirical correlations between peak luminosities and other features that can be observed in the supernovae spectra and their light curves. Such correlations deserve further study since they have been established from small samples of nearby SNIa. Two years ago, the EROS2 collaboration launched an automated search for supernovae with the 1m Marly telescope operating at La Silla. In all, 57 SNe have been discovered in this EROS2 search and spectra have been obtained for 26 of them. We found that 75% were of type Ia and 25% of type II. Using this sample, a preliminary SN explosion rate has been obtained. Our most recent observation campaign took place in February and March 99. It was performed in the framework of a large consortium led by the {\em Supernova Cosmology Project}. The aim of this intensive campaign was to provide an independent set of high quality light curves and spectra to study systematic effects in the measurement of cosmological parameters. We will briefly describe our search procedure and present the status of our ongoing analysis.Comment: 5 page

Quantum Hall fractions in ultracold fermionic vapors

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 wavefunction is then the exact ground state at filling fraction nu=1/3. We give estimates of some of the gaps of the incompressible liquids for nu = p/(2p+-1). We estimate the mass of the composite fermions at nu =1/2. The width of the quantum Hall plateaus is discussed by considering the equation of state of the system.Comment: RevTex, 4 pages, 3 fig

A simple anisotropic three-dimensional quantum spin liquid with fracton topological order

We present a three-dimensional cubic lattice spin model, anisotropic in the $\hat{z}$ direction, that exhibits fracton topological order. The latter is a novel type of topological order characterized by the presence of immobile pointlike excitations, named fractons, residing at the corners of an operator with two-dimensional support. As other recent fracton models, ours exhibits a subextensive ground state degeneracy: On an $L_x\times L_y\times L_z$ three-torus, it has a $2^{2L_z}$ topological degeneracy, and an additional non-topological degeneracy equal to $2^{L_xL_y-2}$. The fractons can be combined into composite excitations that move either in a straight line along the $\hat{z}$ direction, or freely in the $xy$ plane at a given height $z$. While our model draws inspiration from the toric code, we demonstrate that it cannot be adiabatically connected to a layered toric code construction. Additionally, we investigate the effects of imposing open boundary conditions on our system. We find zero energy modes on the surfaces perpendicular to either the $\hat{x}$ or $\hat{y}$ directions, and their absence on the surfaces normal to $\hat{z}$. This result can be explained using the properties of the two kinds of composite two-fracton mobile excitations.Comment: 8 pages, 9 figure

Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in ∣C∣=2|C|=2 flat bands

We perform an exact-diagonalization study of quasihole excitations for the two-component Halperin $(221)$ state in the lowest Landau level and for several $\nu=1/3$ bosonic fractional Chern insulators in topological flat bands with Chern number $|C|=2$. Properties including the quasihole size, charge, and braiding statistics are evaluated. For the Halperin $(221)$ model state, we observe isotropic quasiholes with a clear internal structure, and obtain the quasihole charge and statistics matching the theoretical values. Interestingly, we also extract the same quasihole size, charge, and braiding statistics for the continuum model states of $|C|=2$ fractional Chern insulators, although the latter possess a "color-entangled" nature that does not exist in ordinary two-component Halperin states. We also consider two real lattice models with a band having $|C|=2$. There, we find that a quasihole can exhibit much stronger oscillations of the density profile, while having the same charge and statistics as those in the continuum models.Comment: 11 pages, 10 figures, small changes in the text related to the review process (mostly improved presentation of the color-entangled BC), added bibliographical detail

Entanglement signatures of quantum Hall phase transitions

We study quantum phase transitions involving fractional quantum Hall states, using numerical calculations of entanglements and related quantities. We tune finite-size wavefunctions on spherical geometries, by varying the interaction potential away from the Coulomb interaction. We uncover signatures of quantum phase transitions contained in the scaling behavior of the entropy of entanglement between two parts of the sphere. In addition to the entanglement entropy, we show that signatures of quantum phase transitions also appear in other aspects of the reduced density matrix of one part of the sphere.Comment: 8 pages, 7 figure

Probing many-body localization with neural networks

We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime. Specifically, we study the Heisenberg spin-1/2 chain in a random external field. We employ a multilayer perceptron with a single hidden layer, which is trained on labeled entanglement spectra pertaining to the fully localized and fully thermal regimes. We then apply this network to classify spectra belonging to states in the transition region. For training, we use a cost function that contains, in addition to the usual error and regularization parts, a term that favors a confident classification of the transition region states. The resulting phase diagram is in good agreement with the one obtained by more conventional methods and can be computed for small systems. In particular, the neural network outperforms conventional methods in classifying individual eigenstates pertaining to a single disorder realization. It allows us to map out the structure of these eigenstates across the transition with spatial resolution. Furthermore, we analyze the network operation using the dreaming technique to show that the neural network correctly learns by itself the power-law structure of the entanglement spectra in the many-body localized regime.Comment: 12 pages, 10 figure

Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in ν=1/2+1/2\nu = 1/2 + 1/2 Bilayers

We propose a one-parameter variational ansatz to describe the tunneling-driven Abelian to non-Abelian transition in bosonic $\nu=1/2+1/2$ fractional quantum Hall bilayers. This ansatz, based on exact matrix product states, captures the low-energy physics all along the transition and allows to probe its characteristic features. The transition is continuous, characterized by the decoupling of antisymmetric degrees of freedom. We futhermore determine the tunneling strength above which non-Abelian statistics should be observed experimentally. Finally, we propose to engineer the inter-layer tunneling to create an interface trapping a neutral chiral Majorana. We microscopically characterize such an interface using a slightly modified model wavefunction.Comment: 5 pages, 4 Figures and Supplementary Materials. Comments are welcome

Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition

We address the breakdown of the bulk-boundary correspondence observed in non-Hermitian systems, where open and periodic systems can have distinct phase diagrams. The correspondence can be completely restored by considering the Hamiltonian's singular value decomposition instead of its eigendecomposition. This leads to a natural topological description in terms of a flattened singular decomposition. This description is equivalent to the usual approach for Hermitian systems and coincides with a recent proposal for the classification of non-Hermitian systems. We generalize the notion of the entanglement spectrum to non-Hermitian systems, and show that the edge physics is indeed completely captured by the periodic bulk Hamiltonian. We exemplify our approach by considering the chiral non-Hermitian Su-Schrieffer-Heger and Chern insulator models. Our work advocates a different perspective on topological non-Hermitian Hamiltonians, paving the way to a better understanding of their entanglement structure.Comment: 6+5 pages, 8 figure