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

TL;DR

This paper develops a method to compute form factors of the XXX Heisenberg spin chain in the thermodynamic limit, effectively handling complex Bethe roots and expressing results as finite determinants.

Contribution

It introduces a novel approach to express form factors as finite determinants, including complex roots, within the algebraic Bethe ansatz framework for the thermodynamic limit.

Findings

Form factors expressed as finite determinants in the thermodynamic limit.

Effective treatment of complex Bethe roots.

Gaudin determinant derived from algebraic Bethe ansatz.

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.