# Correlation functions of the XXZ spin chain with the twisted boundary condition

## TL;DR

This paper derives explicit formulas for scalar products, form factors, and correlation functions of the XXZ spin chain with twisted boundary conditions using the Bethe Ansatz, enabling precise analysis of its physical properties.

## Contribution

It introduces a method to compute correlation functions of the XXZ spin chain with twisted boundaries using the inhomogeneous T-Q relation and determinant representations.

## Key findings

- Scalar products and form factors expressed as determinants.
- Correlation functions computed for twisted boundary conditions.
- Results verified through numerical calculations.

## Abstract

The scalar products, form factors and correlation functions of the XXZ spin chain with twisted (or antiperiodic) boundary condition are obtained based on the inhomogeneous $T-Q$ relation and the Bethe states constructed via the off-diagonal Bethe Ansatz. It is shown that the scalar product of two off-shell Bethe states, the form factors and the two-point correlation functions can be expressed as the summation of certain determinants. The corresponding homogeneous limits are studied. The results are also checked by the numerical calculations.