Form factors of integrable higher-spin XXZ chains and the affine quantum-group symmetry

TL;DR

This paper derives exact scalar products and form factors for integrable higher-spin XXZ chains using algebraic Bethe-ansatz, revealing affine quantum-group symmetry and providing tools for studying correlation functions.

Contribution

It introduces a method to compute form factors for arbitrary spin XXZ chains and explicitly derives the diagonalized operators using quantum-group symmetry.

Findings

Exact scalar products and form factors for higher-spin XXZ chains

Explicit diagonalization of B and C operators in the F-basis

Demonstration of affine quantum-group symmetry in the monodromy matrix

Abstract

We derive exactly scalar products and form factors for integrable higher-spin XXZ chains through the algebraic Bethe-ansatz method. Here spin values are arbitrary and different spins can be mixed. We show the affine quantum-group symmetry, $U_q(\hat{sl_2})$, for the monodromy matrix of the XXZ spin chain, and then obtain the exact expressions. Furthermore, through the quantum-group symmetry we explicitly derive the diagonalized forms of the $B$ and $C$ operators in the $F$-basis for the spin-1/2 XXZ spin chain, which was conjectured in the algebraic Bethe-ansatz calculation of the XXZ correlation functions. The results should be fundamental in studying form factors and correlation functions systematically for various solvable models associated with the integrable XXZ spin chains.