Phases of random antiferromagnetic spin-1 chains

We formulate a real-space renormalization scheme that allows the study of the effects of bond randomness in the Heisenberg antiferromagnetic spin-1 chain. There are four types of bonds that appear during the renormalization flow. We implement numerically the decimation procedure. We give a detailed study of the probability distributions of all these bonds in the phases that occur when the strength of the disorder is varied. Approximate flow equations are obtained in the weak-disorder regime as well as in the strong disorder case where the physics is that of the random singlet phase.Comment: 29 pages, 12 encapsulated Postscript figures, REVTeX 3.

Composite fermion theory of rapidly rotating two-dimensional bosons

Ultracold neutral bosons in a rapidly rotating atomic trap have been predicted to exhibit fractional quantum Hall-like states. We describe how the composite fermion theory, used in the description of the fractional quantum Hall effect for electrons, can be applied to interacting bosons. Numerical evidence supporting the formation of composite fermions, each being the bound state of a boson and one flux quantum, is shown for filling fractions of the type nu=p/(p+1), both by spectral analysis and by direct comparison with trial wave functions. The rapidly rotating system of two-dimensional bosons thus constitutes an interesting example of "statistical transmutation," with bosons behaving like composite fermions. We also describe the difference between the electronic and the bosonic cases when p approaches infinity. Residual interactions between composite fermions are attractive in this limit, resulting in a paired composite-fermion state described by the Moore-Read wave function.Comment: 12 pages, 9 figures. Conference proceeding. BEC 2005 Ital

Dorset Harpoon Endblade Hafting and Early Metal Use in the North American Arctic

Composite tool hafting research has touched upon almost every era and region of human history. One aspect that has seen little attention is how those traces of hafting strategies might reflect the raw material of the endblade that an organic handle would have held. This aspect is particularly important for clarifying the scope and scale of novel raw material use in contexts that have concurrent use of different lithic, bone, and metal materials. This article analyzes harpoon heads from the Canadian Arctic in Dorset cultural contexts and identifies three different hafting techniques employed across time. For roughly one millennium, Dorset groups used a single harpoon endblade hafting technique. After AD 500, new hafting techniques were developed, corresponding with the emergence of metal use. Some of these methods are not compatible with common chipped stone materials and signal an increase in metal endblade production. However, surviving metal objects are underrepresented in museum collections because of various taphonomic processes. By recognizing the materials of the harpoon endblade and the specific constraints of some hafting techniques, it is possible to identify what these endblade materials may have been and expand the known extent and intensity of early metal use by observing the hafts alone. Les recherches sur l’emmanchement d’outils composites ont touché presque chaque ère et chaque région de l’histoire humaine. Un aspect qui a reçu peu d’attention a trait à la manière dont les traces des stratégies d’emmanchement pourraient refléter le matériau brut de la pointe qu’un emmanchement organique aurait permis de tenir. Cet aspect est particulièrement important quand vient le temps de préciser la portée et l’échelle de l’utilisation de nouveaux matériaux bruts dans des contextes où se trouve l’usage concurrent de différents matériaux de pierre, d’os et de métal. Cet article analyse les têtes de harpon de contextes culturels du Dorset dans l’Arctique canadien et fait état de trois techniques d’emmanchement différentes employées au fil du temps. Pendant environ un millénaire, les Dorsétiens se sont servis d’une seule technique d’emmanchement des pointes de harpon. Après 500 A.D., de nouvelles techniques d’emmanchement ont vu le jour, correspondant avec l’apparition de l’utilisation du métal. Certaines de ces méthodes ne sont pas compatibles avec les matériaux communs de pierre taillée commune et signalent l’intensification de la production de pointes en métal. Cependant, les objets en métal ayant survécu au passage du temps sont sous-représentés dans les collections de musées en raison de divers processus taphonomiques. En reconnaissant les matériaux de la pointe de harpon et les contraintes particulières découlant de certaines techniques d’emmanchement, il est possible de déterminer ce qu’auraient pu être les matériaux des pointes et d’enrichir l’étendue et l’intensité connues des débuts de l’utilisation du métal seulement en observant les emmanchements.&nbsp

Creation and dynamics of spin fluctuations in a noisy magnetic field

We theoretically and numerically investigate the spin fluctuations induced in a thermal atomic ensemble by an external fluctuating uniaxial magnetic field, in the context of a standard spin noise spectroscopy (SNS) experiment. We show that additional spin noise is excited, which dramatically depends on the magnetic noise variance and bandwidth, as well as on the power of the probe light and its polarization direction. We develop an analytical perturbative model proving that this spin noise first emerges from the residual optical pumping in the medium, which is then converted into spin fluctuations by the magnetic noise and eventually detected using SNS. The system studied is a spin-1 system, which thus shows both Faraday rotation and ellipticity noises induced by the random magnetic fluctuations. The analytical model gives results in perfect agreement with the numerical simulations, with potential applications in future experimental characterization of stray field properties and their influence on spin dynamics.Comment: 16 pages, 10 figures, submitted to New Journal of Physic

On the correct continuum limit of the functional-integral representation for the four-slave-boson approach to the Hubbard model: Paramagnetic phase

The Hubbard model with finite on-site repulsion U is studied via the functional-integral formulation of the four-slave-boson approach by Kotliar and Ruckenstein. It is shown that a correct treatment of the continuum imaginary time limit (which is required by the very definition of the functional integral) modifies the free energy when fluctuation (1/N) corrections beyond mean-field are considered. Our analysis requires us to suitably interpret the Kotliar and Ruckenstein choice for the bosonic hopping operator and to abandon the commonly used normal-ordering prescription, in order to obtain meaningful fluctuation corrections. In this way we recover the exact solution at U=0 not only at the mean-field level but also at the next order in 1/N. In addition, we consider alternative choices for the bosonic hopping operator and test them numerically for a simple two-site model for which the exact solution is readily available for any U. We also discuss how the 1/N expansion can be formally generalized to the four-slave-boson approach, and provide a simplified prescription to obtain the additional terms in the free energy which result at the order 1/N from the correct continuum limit.Comment: Changes: Printing problems (due to non-standard macros) have been removed, 44 page

J1−J2J_1-J_2 quantum Heisenberg antiferromagnet on the triangular lattice: a group symmetry analysis of order by disorder

On the triangular lattice, for $J_2/J_1$ between $1/8$ and $1$, the classical Heisenberg model with first and second neighbor interactions presents four-sublattice ordered ground-states. Spin-wave calculations of Chubukov and Jolicoeur\cite{cj92} and Korshunov\cite{k93} suggest that quantum fluctuations select amongst these states a colinear two-sublattice order. From theoretical requirements, we develop the full symmetry analysis of the low lying levels of the spin-1/2 Hamiltonian in the hypotheses of either a four or a two-sublattice order. We show on the exact spectra of periodic samples ($N=12,16$ and $28$) how quantum fluctuations select the colinear order from the four-sublattice order.Comment: 15 pages, 4 figures (available upon request), Revte

Spin wave theory for antiferromagnetic XXZ spin model on a triangle lattice in the presence of an external magnetic field

Spin wave theory is applied to a quantum antiferromagnetic XXZ model on a triangle lattice in the presence of an in-plane magnetic field. The effect of the field is found to enhance the quantum fluctuation and to reduce the sublattice magnetization at the intermediate field strength in the anisotropic case. The possible implication to the field driven quantum phase transition from a spin solid to a spin liquid is discussed.Comment: 5 pages,4 figure

Highest weight Macdonald and Jack Polynomials

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.Comment: 17 pages, published versio

Perturbative Thermodynamics of Lattice QCD with Chiral-Invariant Four-Fermion Interactions

Lattice QCD with additional chiral-invariant four-fermion interactions is studied at nonzero temperature. Staggered Kogut-Susskind quarks are used. The four-fermion interactions are implemented by introducing bosonic auxiliary fields. A mean field treatment of the auxiliary fields is used to calculate the model's asymptotic scale parameter and perturbative thermodynamics, including the one-loop gluonic contributions to the energy, entropy, and pressure. In this approach the calculations reduce to those of ordinary lattice QCD with massive quarks. Hence, the previous calculations of these quantities in lattice QCD using massless quarks are generalized to the massive case.Comment: 22 pages, RevTeX, 8 EPS figures, uses epsf.sty and feynmf.st