Form factors of the XXZ Heisenberg spin-1/2 finite chain

TL;DR

This paper computes explicit form factors and correlation functions for the finite XXZ Heisenberg spin-1/2 chain using representation theory of quantum affine algebras, providing determinant formulas for these quantities.

Contribution

It introduces a novel method leveraging Drinfel'd twists to derive determinant expressions for form factors and correlation functions in the finite XXZ chain.

Findings

Explicit determinant formulas for form factors derived

Two-point correlation functions calculated

Representation theory techniques applied successfully

Abstract

Form factors for local spin operators of the XXZ Heisenberg spin-1/2 finite chain are computed. Representation theory of Drinfel'd twists for the sl2 quantum affine algebra in finite dimensional modules is used to calculate scalar products of Bethe states (leading to Gaudin formula) and to solve the quantum inverse problem for local spin operators in the finite XXZ chain. Hence, we obtain the representation of the n-spin correlation functions in terms of expectation values(in ferromagnetic reference state) of the operator entries of the quantum monodromy matrix satisfying Yang-Baxter algebra. This leads to the direct calculation of the form factors of the XXZ Heisenberg spin-1/2 finite chain as determinants of usual functions of the parameters of the model. A two-point correlation function for adjacent sites is also derived using similar techniques.