Spinon excitation spectra of the J1J_1-J2J_2 chain from analytical calculations in the dimer basis and exact diagonalization

The excitation spectrum of the frustrated spin-$1/2$ Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at $J_2=0.25J_1$ and an onset of incommensurability in the dispersion relation at $J_2=9/17J_1$ [as in S. Brehmer \emph{et al.}, J. Phys.: Condens. Matter \textbf{10}, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture.Comment: 11 pages, 6 figure

Magnetic responses of randomly depleted spin ladders

The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied using various methods and including the regime where frustration induces incommensurability. Several improvements are made on the results of the seminal work of Sigrist and Furusaki [J. Phys. Soc. Jpn. 65, 2385 (1996)]. Deviations from the Brillouin magnetic curve due to interactions are also analyzed. First, the magnetic profile around a single impurity and effective interactions between impurities are analyzed within the bond-operator mean-field theory and compared to density-matrix renormalization group calculations. Then, the temperature behavior of the Curie constant is studied in details. At zero-temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattice and compute exactly the distribution of ladder cluster due to chain breaking effects. Using exact diagonalization and quantum Monte-Carlo methods on the effective model, the temperature dependence of the Curie constant is compared to a random dimer model and a real-space renormalization group scenario. Next, the low-part of the magnetic curve corresponding to the contribution of impurities is computed using exact diagonalization. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from the Brillouin response. At zero-temperature, the effective model prediction agrees relatively well with density-matrix renormalization group calculations. Finite-temperature effects are displayed within the effective model and for large depleted ladder models using quantum Monte-Carlo simulations. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2PO6 compound and other spin-gapped materials are briefly discussed.Comment: 24 pages, 20 figure

Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder

The phase diagram of an antiferromagnetic ladder with frustrating next-nearest neighbor couplings along the legs is determined using numerical methods (exact diagonalization and density-matrix renormalization group) supplemented by strong-coupling and mean-field analysis. Interestingly, this model displays remarkable features, bridging the physics of the J_1-J_2 chain and of the unfrustated ladder. The phase diagram as a function of the transverse coupling J_{\perp} and the frustration J_2 exhibits an Ising transition between a columnar phase of dimers and the usual rung-singlet phase of two-leg ladders. The transition is driven by resonating valence bond fluctuations in the singlet sector while the triplet spin gap remains finite across the transition. In addition, frustration brings incommensurability in the real-space spin correlation functions, the onset of which evolves smoothly from the J_1-J_2 chain value to zero in the large-J_{\perp} limit. The onset of incommensurability in the spin structure-factor and in the dispersion relation is also analyzed. The physics of the frustrated rung-singlet phase is well understood using perturbative expansions and mean-field theories in the large-J_{\perp} limit. Lastly, we discuss the effect of the non-trivial magnon dispersion relation on the thermodynamical properties of the system. The relation of this model and its physics to experimental observations on compounds which are currently investigated, such as BiCu_2PO_6, is eventually addressed.Comment: 13 pages, 13 figure

How to coexist with fire ants: The roles of behaviour and cuticular compounds

tBecause territoriality is energetically costly, territorial animals frequently respond less aggressively toneighbours than to strangers, a reaction known as the “dear enemy phenomenon” (DEP). The contrary,the “nasty neighbour effect” (NNE), occurs mainly for group-living species defending resource-basedterritories. We studied the relationships between supercolonies of the pest fire ant Solenopsis saevissimaand eight ant species able to live in the vicinity of its nests plus Eciton burchellii, an army ant predatorof other ants. The workers from all of the eight ant species behaved submissively when confrontedwith S. saevissima (dominant) individuals, whereas the contrary was never true. Yet, S. saevissima weresubmissive towards E. burchellii workers. Both DEP and NNE were observed for the eight ant species, withsubmissive behaviours less frequent in the case of DEP. To distinguish what is due to chemical cues fromwhat can be attributed to behaviour, we extracted cuticular compounds from all of the nine ant speciescompared and transferred them onto a number of S. saevissima workers that were then confronted withuntreated conspecifics. The cuticular compounds from three species, particularly E. burchellii, triggeredgreater aggressiveness by S. saevissima workers, while those from the other species did not

De la frustration et du désordre dans les chaînes et les échelles de spins quantiques

Dans les systèmes de spins quantiques, la frustration et la basse dimensionnalité génèrent des fluctuations quantiques et donnent lieu à des phases exotiques. Cette thèse étudie un modèle d'échelle de spins avec des couplages frustrants le long des montants, motivé par les expériences sur le cuprate BiCu$_2$PO$_6$. Dans un premier temps, on présente une méthode variationnelle originale pour décrire les excitations de basse énergie d'une seule chaîne frustrée. Le diagramme de phase de deux chaînes couplées est ensuite établi à l'aide de méthodes numériques. Le modèle exhibe une transition de phase quantique entre une phase dimérisée est une phase à liens de valence résonnants (RVB). La physique de la phase RVB et en particulier l'apparition de l'incommensurabilité sont étudiées numériquement et par un traitement en champ moyen. On étudie ensuite les effets d'impuretés non-magnétiques sur la courbe d'aimantation et la loi de Curie à basse température. Ces propriétés magnétiques sont tout d'abord discutées à température nulle à partir d'arguments probabilistes. Puis un modèle effectif de basse énergie est dérivé dans la théorie de la réponse linéaire et permet de rendre compte des propriétés magnétiques à température finie. Enfin, on étudie l'effet d'un désordre dans les liens, sur une seule chaîne frustrée. La méthode variationnelle, introduite dans le cas non-désordonné, donne une image à faible désordre de l'instabilité de la phase dimérisée, qui consiste en la formation de domaines d'Imry-Ma délimités par des spinons localisés. Ce résultat est finalement discuté à la lumière de la renormalisation dans l'espace réel à fort désordre.In quantum spins systems, frustration and low-dimensionality generate quantum fluctuations and give rise to exotic quantum phases. This thesis studies a spin ladder model with frustrating couplings along the legs, motivated by experiments on cuprate BiCu$_2$PO$_6$. First, we present an original variational method to describe the low-energy excitations of a single frustrated chain. Then, the phase diagram of two coupled chains is computed with numerical methods. The model exhibits a quantum phase transition between a dimerized phase and resonating valence bound (RVB) phase. The physics of the RVB phase and in particular the onset of incommensurability are studied numerically and by a mean-field treatment. Afterwards, we study the effects of non-magnetic impurities on the magnetization curve and the Curie law at low temperature. These magnetic properties are first discussed at zero temperature with probability arguments. Then a low-energy effective model is derived within the linear response theory and is used to explain the magnetic properties at finite temperature. Eventually, we study the effect of bonds disorder, on a single frustrated chain. The variational method introduced in the non-disordered case gives a low disorder picture of the dimerized phase instability, which consists in the formation of Imry-Ma domains delimited by localized spinons. This result is finally discussed in the light of the strong disorder real space renormalization.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

An Overlooked Mandibular-Rubbing Behavior Used during Recruitment by the African Weaver Ant, Oecophylla longinoda

In Oecophylla, an ant genus comprising two territorially dominant arboreal species, workers are known to (1) use anal spots to mark their territories, (2) drag their gaster along the substrate to deposit short-range recruitment trails, and (3) drag the extruded rectal gland along the substrate to deposit the trails used in long-range recruitment. Here we study an overlooked but important marking behavior in which O. longinoda workers first rub the underside of their mandibles onto the substrate, and then—in a surprising posture—tilt their head and also rub the upper side of their mandibles. We demonstrate that this behavior is used to recruit nestmates. Its frequency varies with the rate at which a new territory, a sugary food source, a prey item, or an alien ant are discovered. Microscopy analyses showed that both the upper side and the underside of the mandibles possess pores linked to secretory glands. So, by rubbing their mandibles onto the substrate, the workers probably spread a secretion from these glands that is involved in nestmate recruitment

Internal states of model isotropic granular packings. I. Assembling process, geometry and contact networks

This is the first paper of a series of three, reporting on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. Frictionless systems assemble in the unique random close packing (RCP) state in the low pressure limit if the compression process is fast enough, slower processes inducing traces of crystallization, and exhibit specific properties directly related to isostaticity of the force-carrying structure. The different structures of frictional packings assembled by various methods cannot be classified by the sole density. While lubricated systems approach RCP densities and coordination number z^*~=6 on the backbone in the rigid limit, an idealized "vibration" procedure results in equally dense configurations with z^*~=4.5. Near neighbor correlations on various scales are computed and compared to available laboratory data, although z^* values remain experimentally inaccessible. Low coordination packings have many rattlers (more than 10% of the grains carry no force), which should be accounted for on studying position correlations, and a small proportion of harmless "floppy modes" associated with divalent grains. Frictional packings, however slowly assembled under low pressure, retain a finite level of force indeterminacy, except in the limit of infinite friction.Comment: 29 pages. Published in Physical Review

High efficiency coupling of free electrons to sub-λ3\lambda^3 modal volume, high-Q photonic cavities

We report on the design, realization and experimental investigation by spatially resolved monochromated electron energy loss spectroscopy (EELS) of high quality factor cavities with modal volumes smaller than $\lambda^3$, with $\lambda$ the free-space wavelength of light. The cavities are based on a slot defect in a 2D photonic crystal slab made up of silicon. They are optimized for high coupling of electrons accelerated to 100 kV, to quasi-Transverse Electrical modes polarized along the slot direction. We studied the cavities in two geometries. The first geometry, for which the cavities have been designed, corresponds to an electron beam travelling along the slot direction. The second consists in the electron beam travelling perpendicular to the slab. In both cases, a large series of modes is identified. The dielectric slot modes energies are measured to be in the 0.8- 0.85 eV range, as per design, and surrounded by two bands of dielectric and air modes of the photonic structure. The dielectric even slot modes, to which the cavity mode belongs, are highly coupled to the electrons with up to 3.2$\%$ probability of creating a slot photon per incident electron. Although the experimental spectral resolution (around 30 meV) alone does not allow to disentangle cavity photons from other slot photons, the remarkable agreement between the experiments and FDTD simulations permits us to deduce that amongst the photons created in the slot, around 30$\%$ are stored in the cavity mode. A systematic study of the energy and coupling strength as a function of the photonic band gap parameters permits to foresee increase of coupling strength by fine-tuning phase matching. Our work demonstrates free electron coupling to high quality factor cavities with low mode density, sub-$\lambda^3$ modal volume, making it an excellent candidate for applications such as quantum nano-optics with free electrons

Traitement par nanofiltration d’effluents aqueux polysiloxaniques : influence des matrices salines

Les siloxanes sont utilisés dans tous les domaines de l’industrie. Depuis quelques années, certains pays ont mis en place des règlements encadrant les rejets aqueux siloxaniques. Dans une perspective de développement durable, les industriels sont à la recherche de technologies de traitement pour maîtriser leurs rejets. La nanofiltration paraît particulièrement adaptée pour les caractéristiques de séparation qu’elle autorise en regard de la taille des molécules visées. Cet article présente donc une étude de la nanofiltration pour le traitement des effluents siloxaniques. Les filtrations sont réalisées en mode frontal avec des effluents représentatifs des rejets industriels, caractérisés par une salinité élevée. L’octaméthylcyclotétrasiloxane (D4), molécule de base de la chimie des silicones, est choisie comme composé cible de l’étude. Des études récentes ont montré une sensibilité importante des performances de la nanofiltration à la présence de sels. Ainsi, cette étude porte une attention particulière à cette problématique. Les résultats montrent effectivement une variation des performances d’épuration en fonction de la salinité. Une diminution de l’abattement en carbone organique total (COT) et de la rétention en D4 est observée lorsque l’effluent est dilué. Les mêmes résultats ont été constatés lorsque la salinité de solutions diluées est augmentée