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Theses

Algèbre de réflexion dynamique et modèles intégrables associées.

Abstract : This thesis is embedded in the general theory of quantum integrable models with boundaries, and the development of associated algebraic structures. We first consider the question of the diagonalization of the XXZ hamiltonian with nondiagonal boundaries. We succeed to find the two sets of eigenstates and eigenvalues of the model if the boundaries parameters satisfy two conditions. We introduce then a statistical physics model which we refer to be the face model with a reflecting end. Moreover, we compute exactly its partition function and show that it takes the form of a simple single matrix determinant. We show that these two problems are related through the vertex-face transformation and are solved using a common algebraic structure, the dynamical reflection algebra and its dual. We focus from a mathematical perspective on this algebra in the general elliptic case. Both the co-module evaluation representation and its dual are introduced. We believe that these structures are the key ingredients for the analysis of face models with boundaries. In particular, using the concept of Drinfel'd twists, we show that the partition function of these models has a simple representation in the general case. Finally, we attempt on a 'dynamization' of the Half-Turn-Symmetric vertexmodel. We describe its partition function in terms of the evaluation representation of the dynamical Yang-Baxter algebra, and find a set of conditions that uniquely determine it.
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https://tel.archives-ouvertes.fr/tel-00664076
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Submitted on : Saturday, January 28, 2012 - 6:20:13 PM
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Ghali Filali. Algèbre de réflexion dynamique et modèles intégrables associées.. Physique mathématique [math-ph]. Université de Cergy Pontoise, 2011. Français. ⟨tel-00664076⟩

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