Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions

TL;DR

This paper develops an algebraic framework for solving open spin chains with soliton non-preserving boundaries using the analytical Bethe ansatz, generalizing to arbitrary representations and deriving comprehensive Bethe equations.

Contribution

It introduces an algebraic approach with abstract monodromy and transfer matrices for open SNP spin chains, enabling general Bethe equations for arbitrary representations.

Findings

Derived full generality Bethe equations for open SNP spin chains.

Linked classification of twisted Yangian representations to transfer matrix eigenvalues.

Provided an algebraic framework applicable to various representations.

Abstract

We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe ansatz. It allows us to deal with a generic gl(N) open SNP spin chain possessing on each site an arbitrary representation. As a result, we obtain the Bethe equations in their full generality. The classification of finite dimensional irreducible representations for the twisted Yangians are directly linked to the calculation of the transfer matrix eigenvalues.