Non-linear Integral Equations and Determinant Formulae of the Open XXZ Spin Chain

TL;DR

This paper derives a non-linear integral equation for the open XXZ spin chain's lowest state and combines it with determinant formulas for norms and scalar products, advancing analytical methods in quantum integrable systems.

Contribution

It introduces a new integral equation for the open XXZ chain's ground state and links it with existing determinant formulas, enhancing analytical tools for these models.

Findings

Derived a non-linear integral equation for the lowest state.

Connected integral representation with determinant formulas.

Applicable to open XXZ chains of arbitrary length.

Abstract

We derive a non-linear integral equation for the Bethe-ansatz solvable open XXZ spin chain of arbitrary length describing the lowest lying state with zero magnetization. For this case we show how to combine the integral representation with the known determinant formula of norms and scalar products.