Algebraic Bethe Ansatz for spinor R-matrices

TL;DR

This paper develops a supermatrix representation of q-deformed spinor R-matrices and uses them to analyze transfer matrices of certain quantum spin chains, computing their eigenvectors and eigenvalues.

Contribution

It introduces a supermatrix realization of q-deformed spinor R-matrices and applies this to construct and solve transfer matrices for specific quantum spin chains.

Findings

Eigenvectors and eigenvalues of the transfer matrices are explicitly computed.

The supermatrix realization provides a new approach to analyze q-deformed spinor R-matrices.

The method applies to U_{q^2}(so_{2n+1}) and U_q(so_{2n+2}) symmetric models.

Abstract

We present a supermatrix realisation of q-deformed spinor-spinor and spinor-vector R-matrices. These R-matrices are then used to construct transfer matrices for $U_{q^2}(\mathfrak{so}_{2n+1})$- and $U_{q}(\mathfrak{so}_{2n+2})$-symmetric closed spin chains. Their eigenvectors and eigenvalues are computed.