Quantum teleportation via a two-qubit Heisenberg XXZ chain - effects of anisotropy and magnetic field

We study quantum teleportation via a two-qubit Heisenberg XXZ, chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.

Phase diagram and spectral properties of a new exactly integrable spin-1 quantum chain

The spectral properties and phase diagram of the exactly integrable spin-1 quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated with an unknown R-matrix whose dependence on the spectral parameters is not of a different form. The associated Bethe ansatz equations that fix the eigenspectra are distinct from those associated with other known integrable spin models. The model has a free parameter t(p). We show that at the special point t(p) = 1, the model acquires an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q = exp(i2 pi/3) and in the presence of an external magnetic field. Our analysis is carried out either by solving the associated Bethe ansatz equations or by direct diagonalization of the quantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by the c = 1 conformal field theory separated from a massive phase by first-order phase transitions.

Geometric phase of a bipartite system with Dzyaloshinski-Moriya interaction

The Berry phase of a bipartite system described by a Heisenberg XXZ model driven by a one-site magnetic field is investigated. The effect of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the Berry phase is discussed. It is found that the DM interaction affects the Berry phase monotonously. and can also cause sudden change of the Berry phase for some weak magnetic field cases. (c) 2008 Elsevier B.V. All rights reserved.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

Asymmetric exclusion model with impurities

An integrable asymmetric exclusion process with impurities is formulated. The model displays the full spectrum of the stochastic asymmetric XXZ chain plus new levels. We derive the Bethe equations and calculate the spectral gap for the totally asymmetric diffusion at half filling. While the standard asymmetric exclusion process without impurities belongs to the KPZ universality class with an exponent 3/2, our model has a scaling exponent 5/3.

A(n-1) Gaudin model with open boundaries

The A(n-1) Gaudin model with integrable boundaries specified by non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained. (c) 2005 Elsevier B.V. All rights reserved.

Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field

The thermal entanglement in a two-qubit Heisenberg XXZ spin chain is investigated under an inhomogeneous magnetic field b. We show that the ground-state entanglement is independent of the interaction of z-component J(z). The thermal entanglement at the fixed temperature can be enhanced when J(z) increases. We strictly show that for any temperature T and J(z), the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field b(c) is independent of J(z). The critical magnetic field B-c increases with the increasing parallel to b parallel to but the maximum entanglement value that the system can arrive at becomes smaller.

A two-body study of dynamical expansion in the XXZ spin chain and equivalent interacting fermion models

Lo scopo di questa tesi è studiare l'espansione dinamica di due fermioni interagenti in una catena unidimensionale cercando di definire il ruolo degli stati legati durante l'evoluzione temporale del sistema. Lo studio di questo modello viene effettuato a livello analitico tramite la tecnica del Bethe ansatz, che ci fornisce autovalori ed autovettori dell'hamiltoniana, e se ne valutano le proprietà statiche. Particolare attenzione è stata dedicata alle caratteristiche dello spettro al variare dell'interazione tra le due particelle e alle caratteristiche degli autostati. Dalla risoluzione dell'equazione di Bethe vengono ricercate le soluzioni che danno luogo a stati legati delle due particelle e se ne valuta lo spettro energetico in funzione del momento del centro di massa. Si è studiato inoltre l'andamento del numero delle soluzioni, in particolare delle soluzioni che danno luogo ad uno stato legato, al variare della lunghezza della catena e del parametro di interazione. La valutazione delle proprietà dinamiche del modello è stata effettuata tramite l'utilizzo dell'algoritmo t-DMRG (time dependent - Density Matrix Renormalization Group). Questo metodo numerico, che si basa sulla decimazione dello spazio di Hilbert, ci permette di avere accesso a quantità che caratterizzano la dinamica quali la densità e la velocità di espansione. Da queste sono stati estratti i proli dinamici della densità e della velocità di espansione al variare del valore del parametro di interazione.

Exposants géométriques des modèles de boucles dilués et idempotents des TL-modules de la chaîne de spins XXZ

Cette thèse porte sur les phénomènes critiques survenant dans les modèles bidimensionnels sur réseau. Les résultats sont l'objet de deux articles : le premier porte sur la mesure d'exposants critiques décrivant des objets géométriques du réseau et, le second, sur la construction d'idempotents projetant sur des modules indécomposables de l'algèbre de Temperley-Lieb pour la chaîne de spins XXZ. Le premier article présente des expériences numériques Monte Carlo effectuées pour une famille de modèles de boucles en phase diluée. Baptisés "dilute loop models (DLM)", ceux-ci sont inspirés du modèle O(n) introduit par Nienhuis (1990). La famille est étiquetée par les entiers relativement premiers p et p' ainsi que par un paramètre d'anisotropie. Dans la limite thermodynamique, il est pressenti que le modèle DLM(p,p') soit décrit par une théorie logarithmique des champs conformes de charge centrale c(\kappa)=13-6(\kappa+1/\kappa), où \kappa=p/p' est lié à la fugacité du gaz de boucles \beta=-2\cos\pi/\kappa, pour toute valeur du paramètre d'anisotropie. Les mesures portent sur les exposants critiques représentant la loi d'échelle des objets géométriques suivants : l'interface, le périmètre externe et les liens rouges. L'algorithme Metropolis-Hastings employé, pour lequel nous avons introduit de nombreuses améliorations spécifiques aux modèles dilués, est détaillé. Un traitement statistique rigoureux des données permet des extrapolations coïncidant avec les prédictions théoriques à trois ou quatre chiffres significatifs, malgré des courbes d'extrapolation aux pentes abruptes. Le deuxième article porte sur la décomposition de l'espace de Hilbert \otimes^nC^2 sur lequel la chaîne XXZ de n spins 1/2 agit. La version étudiée ici (Pasquier et Saleur (1990)) est décrite par un hamiltonien H_{XXZ}(q) dépendant d'un paramètre q\in C^\times et s'exprimant comme une somme d'éléments de l'algèbre de Temperley-Lieb TL_n(q). Comme pour les modèles dilués, le spectre de la limite continue de H_{XXZ}(q) semble relié aux théories des champs conformes, le paramètre q déterminant la charge centrale. Les idempotents primitifs de End_{TL_n}\otimes^nC^2 sont obtenus, pour tout q, en termes d'éléments de l'algèbre quantique U_qsl_2 (ou d'une extension) par la dualité de Schur-Weyl quantique. Ces idempotents permettent de construire explicitement les TL_n-modules indécomposables de \otimes^nC^2. Ceux-ci sont tous irréductibles, sauf si q est une racine de l'unité. Cette exception est traitée séparément du cas où q est générique. Les problèmes résolus par ces articles nécessitent une grande variété de résultats et d'outils. Pour cette raison, la thèse comporte plusieurs chapitres préparatoires. Sa structure est la suivante. Le premier chapitre introduit certains concepts communs aux deux articles, notamment une description des phénomènes critiques et de la théorie des champs conformes. Le deuxième chapitre aborde brièvement la question des champs logarithmiques, l'évolution de Schramm-Loewner ainsi que l'algorithme de Metropolis-Hastings. Ces sujets sont nécessaires à la lecture de l'article "Geometric Exponents of Dilute Loop Models" au chapitre 3. Le quatrième chapitre présente les outils algébriques utilisés dans le deuxième article, "The idempotents of the TL_n-module \otimes^nC^2 in terms of elements of U_qsl_2", constituant le chapitre 5. La thèse conclut par un résumé des résultats importants et la proposition d'avenues de recherche qui en découlent.

Analysis of the spectrum of the spin-1 biquadratic antiferromagnetic chain

In questo elaborato vengono discusse le catene di spin-1, modelli quantistici definiti su un reticolo unidimensionale con interazione tra siti primi vicini. Fra la ricca varietà di tipologie esistenti è stato scelto di porre attenzione primariamente sul modello antiferromagnetico con interazione puramente biquadratica. Vengono presentati diversi metodi di classificazione degli autostati di tale modello, a partire dalle simmetrie che ne caratterizzano l’Hamiltoniana. La corrispondenza con altri modelli noti, quali il modello XXZ di spin 1/2, la catena di Heisenberg SU (3) ed i modelli di Potts, è utile ad individuare strutture simmetriche nascoste nel formalismo di spin-1, le quali consentono di ricavare informazioni sullo spettro energetico. Infine, vengono presentati risultati numerici accompagnati da alcune considerazioni sulle modifiche dello spettro quando si aggiunge un termine bilineare alla Hamiltoniana biquadratica.

T-Q relation and exact solution for the XYZ chain with general non-diagonal boundary terms

We propose that the Baxter's Q-operator for the quantum XYZ spin chain with open boundary conditions is given by the j -> infinity limit of the corresponding transfer matrix with spin-j (i.e., (2j + I)-dimensional) auxiliary space. The associated T-Q relation is derived from the fusion hierarchy of the model. We use this relation to determine the Bethe Ansatz solution of the eigenvalues of the fundamental transfer matrix. The solution yields the complete spectrum of the Hamiltonian. (c) 2006 Elsevier B.V. All rights reserved.

Collaboration and Engagement Throughout The Supply Chain : The Role of Government

Collaboration is acknowledged as a key to continued growth in the Australian construction industry. Government, as a major industry client, has an important role to play with respect to fostering collaboration and ensuring the global competitiveness of the industry. The paper draws upon data collected for the Construction 2020 study and aims to demonstrate that government can a) help to break down the adversarial situation that currently exists between clients, project managers and subcontractors; and b) allow the supply chain to collaborate more effectively in terms of satisfying the relational and financial needs of all parties. Government can also provide a clear set of guidelines (backed up by a functional dispute resolution system) that will promote confidence with respect to forging relationships. Thus, the paper will discuss the way in which public policy can be more closely aligned with actual industry needs in order to promote greater collaboration.