Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model

We study the ground state properties of the critical Lipkin-Meshkov-Glick model. Using the Holstein-Primakoff boson representation, and the continuous unitary transformation technique, we compute explicitly the finite-size scaling exponents for the energy gap, the ground state energy, the magnetization, and the spin-spin correlation functions. Finally, we discuss the behavior of the two-spin entanglement in the vicinity of the phase transition.Comment: 4 pages, published versio

Landau levels in quasicrystals

Two-dimensional tight-binding models for quasicrystals made of plaquettes with commensurate areas are considered. Their energy spectrum is computed as a function of an applied perpendicular magnetic field. Landau levels are found to emerge near band edges in the zero-field limit. Their existence is related to an effective zero-field dispersion relation valid in the continuum limit. For quasicrystals studied here, an underlying periodic crystal exists and provides a natural interpretation to this dispersion relation. In addition to the slope (effective mass) of Landau levels, we also study their width as a function of the magnetic flux per plaquette and identify two fundamental broadening mechanisms: (i) tunneling between closed cyclotron orbits and (ii) individual energy displacement of states within a Landau level. Interestingly, the typical broadening of the Landau levels is found to behave algebraically with the magnetic field with a nonuniversal exponent.Comment: 14 pages, 9 figure

Emergent Fermions and Anyons in the Kitaev Model

We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations. The effective low-energy Hamiltonian is found to be an extended toric code with interacting anyons. High-energy excitations are emerging free fermions which are composed of hardcore bosons with an attached string of spin operators. The excitation spectrum is mapped onto that of a single particle hopping on a square lattice in a magnetic field. We also illustrate how to compute correlation functions in this framework. The present approach yields analytical perturbative results in the thermodynamical limit without using the Majorana or the Jordan-Wigner fermionization initially proposed to solve this problem.Comment: 4 pages, 5 figures, published versio

Une approche conduite par les modèles pour le traçage des activités des utilisateurs dans des EIAH hétérogènes

Cet article propose une approche conduite par les modèles pour la gestion des traces d'activité des utilisateurs au sein de systèmes d'apprentissage hétérogènes instrumentés par les technologies Web. Un modèle UML générique de traces permet de structurer et d'ajouter une sémantique claire aux données observées, auquel est associée une architecture distribuée et décentralisée favorisant le partage et la réutilisation des traces collectées par différents outils et services. Nous appliquons ensuite cette approche au traçage de l'utilisation des objets pédagogiques par des utilisateurs exploitant des plates-formes d'apprentissage et viviers de connaissance. Enfin nous proposons une application pour la visualisation des traces collectées, ainsi qu'un service de recherche avancée d'objets pédagogiques qui offre l'opportunité de capitaliser les expériences d'une large communauté d'utilisateurs

Fédération de ressources pédagogiques

La virtualisation des ressources pédagogiques est devenue un aspect crucial de l'EIAH, et ce pour plusieurs raisons : (a) atteindre cet objectif pour faire face à l'évolution rapide des technologies et une nécessité d'apprentissage et de savoir-faire primordiale pour la survie de tous, (b) rendre nos outils attractifs et pérennes, et (c) se répartir la construction d'un patrimoine de ressources pédagogiques. De nombreux systèmes d'apprentissage existent aujourd'hui mais leurs ressources pédagogiques restent, le plus souvent, cloisonnées au sein de ces systèmes. Nous présentons dans cet article une architecture ouverte basée sur les standards prédominants de la FOAD, et qui supporte les fonctionnalités nécessaires à la virtualisation de ressources pédagogiques. Aussi nous exposons une expérimentation validant l'architecture proposée et qui offre une fédération de deux systèmes indépendants

Sharing Learners' Behavior to Enhance a Metacognition-oriented Intelligent Tutoring System

International audienceLiterature shows that Intelligent Tutoring Systems (ITS) are growing in acceptance and popularity because they increase performances of students, leverage cognitive development, but also significantly reduce time to acquire knowledge and competencies. Moreover, monitoring metacognitive skills enables learners to assess performance and select appropriate fix-up: individuals unable to ensure self-monitoring cannot detect errors and as a consequence, they process information less efficiently than skilled monitors. Thus, we present an ITS offering the opportunity of evaluating various metacognitive indicators and able to share this information with others learning tools. Our online tutor is based on an existing ITS authoring tool that we extended to support metacognition and share learners’ profiles and activities into a standardized, distributed and open tracking repository. This framework, validated by an experimentation, thus helps to correlate metadata experiences with real performanc

Concurrence in collective models

We review the entanglement properties in collective models and their relationship with quantum phase transitions. Focusing on the concurrence which characterizes the two-spin entanglement, we show that for first-order transition, this quantity is singular but continuous at the transition point, contrary to the common belief. We also propose a conjecture for the concurrence of arbitrary symmetric states which connects it with a recently proposed criterion for bipartite entanglement.Comment: 8 pages, 2 figures, published versio

Bridging Perturbative Expansions with Tensor Networks

We demonstrate that perturbative expansions for quantum many-body systems can be rephrased in terms of tensor networks, thereby providing a natural framework for interpolating perturbative expansions across a quantum phase transition. This approach leads to classes of tensor-network states parametrized by few parameters with a clear physical meaning, while still providing excellent variational energies. We also demonstrate how to construct perturbative expansions of the entanglement Hamiltonian, whose eigenvalues form the entanglement spectrum, and how the tensor-network approach gives rise to order parameters for topological phase transitions.Comment: published versio

Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking

We analyze the Kitaev model on the triangle-honeycomb lattice whose ground state has recently been shown to be a chiral spin liquid. We consider two perturbative expansions: the isolated-dimer limit containing Abelian anyons and the isolated-triangle limit. In the former case, we derive the low-energy effective theory and discuss the role played by multi-plaquette interactions. In this phase, we also compute the spin-spin correlation functions for any vortex configuration. In the isolated-triangle limit, we show that the effective theory is, at lowest nontrivial order, the Kitaev honeycomb model at the isotropic point. We also compute the next-order correction which opens a gap and yields non-Abelian anyons.Comment: 7 pages, 4 figures, published versio

Interactions in Quasicrystals

Although the effects of interactions in solid state systems still remains a widely open subject, some limiting cases such as the three dimensional Fermi liquid or the one-dimensional Luttinger liquid are by now well understood when one is dealing with interacting electrons in {\it periodic} crystalline structures. This problem is much more fascinating when periodicity is lacking as it is the case in {\it quasicrystalline} structures. Here, we discuss the influence of the interactions in quasicrystals and show, on a controlled one-dimensional model, that they lead to anomalous transport properties, intermediate between those of an interacting electron gas in a periodic and in a disordered potential.Comment: Proceedings of the Many Body X conference (Seattle, Sept. 99); 9 pages; uses epsfi