Determinant Representations for Correlation Functions of Spin-1/2 XXX and XXZ Heisenberg Magnets

TL;DR

This paper derives determinant representations for correlation functions of spin-1/2 XXX and XXZ Heisenberg chains in a magnetic field using algebraic Bethe Ansatz, facilitating analytical and numerical analysis.

Contribution

It introduces a novel method to express correlation functions as determinants of Fredholm integral operators for these models.

Findings

Determinant formulas for correlation functions derived

Applicable to both XXX and XXZ Heisenberg chains

Enhances analytical and computational approaches

Abstract

We consider correlation functions of the spin-$\half$ XXX and XXZ Heisenberg chains in a magnetic field. Starting from the algebraic Bethe Ansatz we derive representations for various correlation functions in terms of determinants of Fredholm integral operators.