Jordanian deformation of the open XXX-spin chain

TL;DR

This paper derives the reflection equation solution for the jordanian-deformed XXX-spin chain, explores its spectrum, and connects it to the XXZ-model through a scaling limit, providing explicit Hamiltonian formulations.

Contribution

It presents the first explicit solution to the reflection equation for the jordanian-deformed XXX-spin chain and derives its Hamiltonian with boundary terms.

Findings

Solution to the reflection equation for the jordanian deformation

Explicit Hamiltonian with boundary terms derived

Spectrum structure depends on boundary conditions

Abstract

The general solution to the reflection equation associated with the jordanian deformation of the SL(2) invariant Yang R-matrix is found. The same K-matrix is obtained by the special scaling limit of the XXZ-model with general boundary conditions. The Hamiltonian with the boundary terms is explicitly derived according to the Sklyanin formalism. We discuss the structure of the spectrum of the deformed XXX-model and its dependence on the boundary conditions.