Non-diagonal solutions to reflection equations in $su(n)$ spin chains

TL;DR

This paper investigates non-diagonal solutions to reflection equations in $su(n)$ spin chains, providing explicit solutions for $su(3)$ and generalizing to higher $su(n)$, with implications for boundary conditions and Hamiltonian formulations.

Contribution

It introduces new non-diagonal solutions to reflection equations in $su(n)$ spin chains, expanding the understanding of boundary conditions in integrable models.

Findings

Found non-diagonal solutions for $su(3)$ reflection equations.

Generalized solutions to $su(n)$ boundary matrices.

Derived the corresponding Hamiltonian for these solutions.

Abstract

The reflection equations in a $su(3)$ spin chain with open boundary conditions are analyzed. We find non diagonal solutions to the boundary matrices. The corresponding hamiltonian is given. The solutions are generalized to $su(n)$.