Scattering matrices in the sl(3) twisted Yangian

TL;DR

This paper analyzes a quantum spin chain with soliton non-preserving boundary conditions using the twisted Yangian algebra, deriving scattering amplitudes and excitation properties via Bethe ansatz in the thermodynamic limit.

Contribution

It introduces a detailed analysis of scattering matrices for the sl(3) twisted Yangian with non-traditional boundary conditions, including explicit calculations of scattering amplitudes.

Findings

Explicit bulk and boundary scattering amplitudes derived.

Quantization conditions for the scattering process formulated.

Energy levels and quantum numbers of low-lying excitations determined.

Abstract

A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected to the boundary, hence the appellation soliton non-preserving boundary conditions. We focus on the simplest non-trivial case of this class of models based on the twisted Yangian quadratic algebra. Our computations are performed through the Bethe ansatz equations in the thermodynamic limit. We formulate a suitable quantization condition describing the scattering process and proceed with explicitly determining the bulk and boundary scattering amplitudes. The energy and quantum numbers of the low lying excitations are also derived.