Correlation functions of the open XXZ chain I

TL;DR

This paper develops a method to compute correlation functions in the open XXZ spin chain with diagonal boundaries using algebraic Bethe Ansatz, resulting in explicit integral formulas similar to the periodic case.

Contribution

It provides explicit integral formulas for correlation functions of the open XXZ chain, extending techniques from periodic boundary conditions.

Findings

Correlation functions expressed as multiple integrals

Explicit computation of scalar products of Bethe states

Extension of bulk inverse problem to open chains

Abstract

We consider the XXZ spin chain with diagonal boundary conditions in the framework of algebraic Bethe Ansatz. Using the explicit computation of the scalar products of Bethe states and a revisited version of the bulk inverse problem, we calculate the elementary building blocks for the correlation functions. In the limit of half-infinite chain, they are obtained as multiple integrals of usual functions, similar to the case of periodic boundary conditions.