A recursion formula for the correlation functions of an inhomogeneous XXX model

TL;DR

This paper introduces a new recursion formula for calculating correlation functions in the inhomogeneous spin 1/2 XXX chain, enabling a direct proof of their structural properties and providing an exact description of associated rational functions.

Contribution

It presents a novel recursion relation for inhomogeneous XXX model correlation functions, advancing understanding of their structure and explicitly determining related rational functions.

Findings

Derived a recursion formula linking n-site correlators to fewer sites

Proved the specific structure of correlators as functions of inhomogeneity parameters

Provided an exact description of the rational functions involved

Abstract

A new recursion formula is presented for the correlation functions of the integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators involving n consecutive lattice sites to those with n-1 and n-2 sites. In a series of papers by V. Korepin and two of the present authors, it was discovered that the correlators have a certain specific structure as functions of the inhomogeneity parameters. Our formula allows for a direct proof of this structure, as well as an exact description of the rational functions which has been left undetermined in the previous works.