Asymptotic analysis of the form-factors of 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 for the computation of the form-factors in thermodynamic limit. It is both applied to and described in the context of isotropic XXX Heisenberg chain, which is one of the examples 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 a higher-level structure for the form-factors is revealed.

arXiv commentPhD Thesis of University of Burgundy, 228 pages, in English with a short introduction in French

References in corpus (19)

• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Correlation Functions of the XXZ model for $\Delta <-1$
• QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime
• On the quantum inverse scattering problem
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Form factor approach to dynamical correlation functions in critical models
• The 4-spinon dynamical structure factor of the Heisenberg chain
• On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain
• Exact two-spinon dynamical correlation function of the Heisenberg model
• Exact two-spin dynamic structure factor of the one-dimensional s=1/2 Heisenberg-Ising antiferromagnet
• On correlation functions of integrable models associated to the six-vertex R-matrix
• Algebraic Bethe ansatz for singular solutions
• Fermionic structure in the sine-Gordon model: form factors and null-vectors
• Exact four-spinon dynamical correlation function of the Heisenberg model
• Form factors of integrable Heisenberg (higher) spin chains
• On form-factor expansions for the XXZ chain in the massive regime
• Exact Form-Factor Results for the Longitudinal Structure Factor of the Massless XXZ Model in Zero Field
• Violations of the String Hypothesis in the Solutions of the Bethe Ansatz Equations in the XXX-Heisenberg
• The exact two-spinon longitudinal dynamical structure factor of the anisotropic XXZ model

Cited by in corpus (2)

• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots