Jordanian deformation of the open sl(2) Gaudin model

TL;DR

This paper derives a Jordanian-deformed version of the open sl(2) Gaudin model with integrable boundaries, expanding the class of exactly solvable models in quantum integrable systems.

Contribution

It introduces a novel Jordanian deformation of the sl(2) Gaudin model with boundary conditions, based on the Jordanian deformation of the Yang R-matrix.

Findings

Derived the deformed Gaudin Hamiltonians with boundary terms

Established the connection with the inhomogeneous spin-1/2 XXX chain

Provided explicit solutions to the reflection equations

Abstract

We derive the deformed sl(2) Gaudin model with integrable boundaries. Starting from the Jordanian deformation of the SL(2)-invariant Yang R-matrix and generic solutions of the associated reflection equation and the dual reflection equation, the corresponding inhomogeneous spin-1/2 XXX chain is obtained. The quasi-classical expansion of the transfer matrix yields the deformed sl(2) Gaudin Hamiltonians with boundary terms.