The integrable quantum group invariant A2n−1 (2) and Dn+1 (2) open spin chains

Abstract

A family of A2n (2) integrable open spin chains with Uq(Cn) symmetry was recently identified in arXiv:1702.01482. We identify here in a similar way a family of A2n−1 (2) integrable open spin chains with Uq(Dn) symmetry, and two families of Dn+1 (2) integrable open spin chains with Uq(Bn) symmetry. We discuss the consequences of these symmetries for the degeneracies and multiplicities of the spectrum. We propose Bethe ansatz solutions for two of these models, whose completeness we check numerically for small values of n and chain length N. We find formulas for the Dynkin labels in terms of the numbers of Bethe roots of each type, which are useful for determining the corresponding degeneracies. In an appendix, we briefly consider Dn+1 (2) chains with other integrable boundary conditions, which do not have quantum group symmetry.