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Asymptotic analysis of the form-factors of the quantum spin chains

Abstract : Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic, of the correlation function is one of the most important subject of the theory of the quantum integrable models. In this context an approach based on the calculation of form factors has been proved to be a more effective one. In this thesis, we develop a new method based on the algebraic Bethe ansatz is proposed for the computation of the form-factors in thermodynamic limit. It is applied to and described in the context of isotropic XXX Heisenberg chain, which is one of the example of an interesting case of critical models where the Fermi-zone is non-compact. In a particular case of two-spinon form-factors, we obtain an exact result in a closed-form which matches the previous result obtained from an approach based on $q$-vertex operator algebra. This method is then generalised to form-factors in higher spinon sectors where we find a reduced determinant representation for the form-factors, in which we find that a higher-level structure for form-factors is revealed.
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Submitted on : Tuesday, March 9, 2021 - 8:57:08 AM
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Giridhar Kulkarni. Asymptotic analysis of the form-factors of the quantum spin chains. General Mathematics [math.GM]. Université Bourgogne Franche-Comté, 2020. English. ⟨NNT : 2020UBFCK043⟩. ⟨tel-03163048⟩

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