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

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 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.