Spinorial R operator and Algebraic Bethe Ansatz

TL;DR

This paper introduces a novel approach to the spinor-spinor R-matrix with orthogonal and symplectic symmetry, relating it to vector R-matrices and the Algebraic Bethe Ansatz for quantum spin chains.

Contribution

It develops a new method for analyzing spinor R-matrices and connects the Bethe Ansatz solutions for spinor and vector monodromy matrices.

Findings

Explicit spinor R matrices for low-rank orthogonal algebras derived

Relations established between spinor and vector monodromy matrices

Connections made between spinor and fundamental R matrices

Abstract

We propose a new approach to the spinor-spinor R-matrix with orthogonal and symplectic symmetry. Based on this approach and the fusion method we relate the spinor-vector and vector-vector monodromy matrices for quantum spin chains. We consider the explicit spinor R matrices of low rank orthogonal algebras and the corresponding RTT algebras. Coincidences with fundamental R matrices allow to relate the Algebraic Bethe Ansatz for spinor and vector monodromy matrices.