General boundary conditions for the sl(N) and sl(M|N) open spin chains

TL;DR

This paper investigates boundary conditions in open sl(n) and sl(m|n) spin chains, classifies solutions, and derives symmetry and Bethe Ansatz equations, including non-diagonal cases and their relation to twisted Yangians.

Contribution

It provides a comprehensive classification of boundary conditions, formulates reflection equations, and explores the connection to twisted super Yangians for these spin chains.

Findings

Classified solutions to reflection equations for both boundary types

Derived symmetry and Bethe Ansatz equations for each case

Analyzed non-diagonal reflection matrices and their algebraic structures

Abstract

Two types of boundary conditions ("soliton preserving" and "soliton non-preserving") are investigated for the sl(n) and sl(m|n) open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe Ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated to "soliton preserving" case is worked out. The connection between the "soliton non-preserving" boundary conditions and the twisted (super) Yangians is also discussed.