Applications de l'ansatz de Bethe Algébrique et au-delà

Abstract : In this thesis, we will discuss quantum integrable systems and spin chains. We will present the notion of quantum integrability and a related algebraic structure, the quantum group. This study allows us to introduce the " universal " spin chains used by the Annecy group few years ago. These " universal " chains encompass all the spins chains studied in the literature. The purpose of this thesis is to evaluate, with the algebraic Bethe ansatz (ABA), the eigenvalues and eigenvectors of these " universal " spins chains. We will discuss the case of closed and open spin chains. This study will highlight the limit of the ABA for open spins chains and we will present a new mathematical framework that may allow to find the spectral problem in this case. We will also discuss the computation of the scalar product between two eigenvectors obtained with the ABA.
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Physique mathématique [math-ph]. Université de Savoie, 2009. Français
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  • HAL Id : tel-00612909, version 1



S. Belliard. Applications de l'ansatz de Bethe Algébrique et au-delà. Physique mathématique [math-ph]. Université de Savoie, 2009. Français. 〈tel-00612909〉



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