Chiral SU(2)_k currents as local operators in vertex models and spin chains

The six-vertex model and its spin-$S$ descendants obtained from the fusion procedure are well-known lattice discretizations of the SU$(2)_k$ WZW models, with $k=2S$. It is shown that, in these models, it is possible to exhibit a local observable on the lattice that behaves as the chiral current $J^a(z)$ in the continuum limit. The observable is built out of generators of the su$(2)$ Lie algebra acting on a small (finite) number of lattice sites. The construction works also for the multi-critical quantum spin chains related to the vertex models, and is verified numerically for $S=1/2$ and $S=1$ using Bethe Ansatz and form factors techniques.Comment: 31 pages, 7 figures; published versio

The Z2Z_2 staggered vertex model and its applications

New solvable vertex models can be easily obtained by staggering the spectral parameter in already known ones. This simple construction reveals some surprises: for appropriate values of the staggering, highly non-trivial continuum limits can be obtained. The simplest case of staggering with period two (the $Z_2$ case) for the six-vertex model was shown to be related, in one regime of the spectral parameter, to the critical antiferromagnetic Potts model on the square lattice, and has a non-compact continuum limit. Here, we study the other regime: in the very anisotropic limit, it can be viewed as a zig-zag spin chain with spin anisotropy, or as an anyonic chain with a generic (non-integer) number of species. From the Bethe-Ansatz solution, we obtain the central charge $c=2$, the conformal spectrum, and the continuum partition function, corresponding to one free boson and two Majorana fermions. Finally, we obtain a massive integrable deformation of the model on the lattice. Interestingly, its scattering theory is a massive version of the one for the flow between minimal models. The corresponding field theory is argued to be a complex version of the $C_2^{(2)}$ Toda theory.Comment: 38 pages, 14 figures, 3 appendice

Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models

In two-dimensional loop models, the scaling properties of critical random curves are encoded in the correlators of connectivity operators. In the dense O($n$) loop model, any such operator is naturally associated to a standard module of the periodic Temperley-Lieb algebra. We introduce a new family of representations of this algebra, with connectivity states that have two marked points, and argue that they define the fusion of two standard modules. We obtain their decomposition on the standard modules for generic values of the parameters, which in turn yields the structure of the operator product expansion of connectivity operators

Local height probabilities in a composite Andrews-Baxter-Forrester model

We study the local height probabilities in a composite height model, derived from the restricted solid-on-solid model introduced by Andrews, Baxter and Forrester, and their connection with conformal field theory characters. The obtained conformal field theories also describe the critical behavior of the model at two different critical points. In addition, at criticality, the model is equivalent to a one-dimensional chain of anyons, subject to competing two- and three-body interactions. The anyonic-chain interpretation provided the original motivation to introduce the composite height model, and by obtaining the critical behaviour of the composite height model, the critical behaviour of the anyonic chains is established as well. Depending on the overall sign of the hamiltonian, this critical behaviour is described by a diagonal coset-model, generalizing the minimal models for one sign, and by Fateev-Zamolodchikov parafermions for the other.Comment: 34 pages, 5 figures; v2: expanded introduction, references added and other minor change

Spin interfaces in the Ashkin-Teller model and SLE

We investigate the scaling properties of the spin interfaces in the Ashkin-Teller model. These interfaces are a very simple instance of lattice curves coexisting with a fluctuating degree of freedom, which renders the analytical determination of their exponents very difficult. One of our main findings is the construction of boundary conditions which ensure that the interface still satisfies the Markov property in this case. Then, using a novel technique based on the transfer matrix, we compute numerically the left-passage probability, and our results confirm that the spin interface is described by an SLE in the scaling limit. Moreover, at a particular point of the critical line, we describe a mapping of Ashkin-Teller model onto an integrable 19-vertex model, which, in turn, relates to an integrable dilute Brauer model.Comment: 12 pages, 6 figure

Integrability as a consequence of discrete holomorphicity: the Z_N model

It has recently been established that imposing the condition of discrete holomorphicity on a lattice parafermionic observable leads to the critical Boltzmann weights in a number of lattice models. Remarkably, the solutions of these linear equations also solve the Yang-Baxter equations. We extend this analysis for the Z_N model by explicitly considering the condition of discrete holomorphicity on two and three adjacent rhombi. For two rhombi this leads to a quadratic equation in the Boltzmann weights and for three rhombi a cubic equation. The two-rhombus equation implies the inversion relations. The star-triangle relation follows from the three-rhombus equation. We also show that these weights are self-dual as a consequence of discrete holomorphicity.Comment: 11 pages, 7 figures, some clarifications and a reference adde

An integrable modification of the critical Chalker-Coddington network model

We consider the Chalker-Coddington network model for the Integer Quantum Hall Effect, and examine the possibility of solving it exactly. In the supersymmetric path integral framework, we introduce a truncation procedure, leading to a series of well-defined two-dimensional loop models, with two loop flavours. In the phase diagram of the first-order truncated model, we identify four integrable branches related to the dilute Birman-Wenzl-Murakami braid-monoid algebra, and parameterised by the loop fugacity $n$. In the continuum limit, two of these branches (1,2) are described by a pair of decoupled copies of a Coulomb-Gas theory, whereas the other two branches (3,4) couple the two loop flavours, and relate to an $SU(2)_r \times SU(2)_r / SU(2)_{2r}$ Wess-Zumino-Witten (WZW) coset model for the particular values $n= -2\cos[\pi/(r+2)]$ where $r$ is a positive integer. The truncated Chalker-Coddington model is the $n=0$ point of branch 4. By numerical diagonalisation, we find that its universality class is neither an analytic continuation of the WZW coset, nor the universality class of the original Chalker-Coddington model. It constitutes rather an integrable, critical approximation to the latter.Comment: 34 pages, 18 figures, 3 appendice

ANALYSE LES PERFORMANCES D’UN SYSTÈME DS-OCDMA EN UTILISANT LES CODES OPTIQUE ORTHOGONAUX (OOC)

In a DS-OCDMA system, the MAI is one of the major limitations due to the unipolarity of the codes used. To mitigate the MAI, several techniques are developed for receptions eliminate the contribution of unwanted users. In this work, we studied the characteristics of correlations OOC codes, and we presented three structures of receptors that are well placed to estimate the information bits. For this, we have developed the theoretical BER expressions error probability

Algorithmes à norme constante pour les systèmes de communication MIMO

- Un nouvel algorithme de séparation aveugle de sources pour les systèmes MIMO (Multiple-Input Multiple-Output) de type BLAST (Bell Labs Layered Space-Time) est proposé, basé sur un critère de norme constante CN (Constant Norm), associé à la procédure d'orthogonalisation de Gram-Schmidt afin d'assurer l'indépendance des sorties de l'égaliseur. De cette approche deux nouveaux algorithmes sont déduits. Le premier appelé CQA (Constant sQuare Algorithm), est mieux adapté pour les modulations QAM que le classique CMA (Constant Modulus Algorithm), il fournit un niveau de bruit plus faible avec une complexité comparable. Le second est une pondération entre le CMA et le CQA pour tirer avantage des deux. Le coefficient de pondération est évalué dynamiquement, d'où son nom de CDNA (Constant Dynamic Norm Algorithm). Les algorithmes proposés reposent sur la minimisation d'une fonction de coût, construite à partir de normes, par un gradient stochastique sous la contrainte d'orthogonalité. En simulation, ces algorithmes montrent de meilleures performances comparés aux algorithmes CMA et MUK avec une complexité comparable. Le CQA atteint un meilleur état permanent que le CMA (gain de 3 dB) et le CDNA tend vers le meilleur algorithme dynamiquement entre le CMA et le CQA

Analyse Des réseaux De Bragg Superposés Pour l’encodage OCDMA. Utilisation Des Codes à Séquences premières

Cet article présente une nouvelle méthode de codage fréquentielle pour le CDMA optique à base de réseaux de Bragg superposés travaillant en réflexion. Des codes à séquences premières PS non cohérent, générées et décodées de manière « tout optique» par un composant spécifique. Le composant consiste en une succession de réseaux de Bragg inscrits sur une fibre optique à différentes longueurs d’onde et à des positions bien définis sur la fibre prédéfinie. L’ordre, ainsi que le choix des longueurs d’onde de ces réseaux de Bragg déterminent le code. La méthode des matrices de transfert a été retenue pour étudier et modéliser un réseau unique ou des réseaux superposés