Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 112, 25 pages      arXiv:2105.10244      https://doi.org/10.3842/SIGMA.2021.112
Contribution to the Special Issue on Mathematics of Integrable Systems: Classical and Quantum in honor of Leon Takhtajan

Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots

Nikolai Kitanine and Giridhar Kulkarni
Institut de Mathématiques de Bourgogne, UMR 5584, CNRS, Université Bourgogne Franche-Comté, F-21000 Dijon, France

Received May 28, 2021, in final form December 17, 2021; Published online December 25, 2021

Abstract
In this article we study the thermodynamic limit of the form factors of the $XXX$ Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite dimensional in the thermodynamic limit. We show how to treat all types of the complex roots of the Bethe equations within this framework. In particular we demonstrate that the Gaudin determinant for the higher level Bethe equations arises naturally from the algebraic Bethe ansatz.

Key words: spin chains; form factors; correlation functions; algebraic Bethe ansatz.

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