Nonstandard Bethe Ansatz equations for open O(N) spin chains

TL;DR

This paper derives nonstandard Bethe Ansatz equations for open O(N) spin chains with specific boundary conditions, revealing how boundary symmetry breaking affects the structure of solutions.

Contribution

It extends the algebraic Bethe Ansatz method to include cases with residual O(2M+1)×O(2N-2M-1) symmetry, previously unaddressed.

Findings

Derived Bethe Ansatz equations for new boundary symmetry cases

Identified reduction in Bethe roots due to boundary effects

Linked boundary symmetry breaking to soliton-nonpreserving reflections

Abstract

The double row transfer matrix of the open O(N) spin chain is diagonalized and the Bethe Ansatz equations are also derived by the algebraic Bethe Ansatz method including the so far missing case when the residual symmetry is O(2M+1)$\times$O(2N-2M-1). In this case the boundary breaks the "rank" of the O(2N) symmetry leading to nonstandard Bethe Ansatz equations in which the number of Bethe roots is less than as it was in the periodic case. Therefore these cases are similar to soliton-nonpreserving reflections.