Trigonometric sl(2) Gaudin model with boundary terms

TL;DR

This paper reviews the derivation of the Gaudin model with boundary terms, starting from the XXZ chain and reflection equations, and discusses an alternative derivation using the classical reflection equation.

Contribution

It introduces a comprehensive derivation of the Gaudin model with boundary terms from the XXZ chain and explores an alternative approach via the classical reflection equation.

Findings

Explicit Gaudin Hamiltonians with boundary terms derived

Connection established between XXZ chain and Gaudin model with boundaries

Alternative derivation method using classical reflection equation discussed

Abstract

We review the derivation of the Gaudin model with integrable boundaries. Starting from the non-symmetric R-matrix of the inhomogeneous spin-1/2 XXZ chain and generic solutions of the reflection equation and the dual reflection equation, the corresponding Gaudin Hamiltonians with boundary terms are calculated. An alternative derivation based on the so-called classical reflection equation is discussed.