### Abstract

A family of A_{2n} ^{(2)} integrable open spin chains with U_{q}(C_{n}) symmetry was recently identified in arXiv:1702.01482. We identify here in a similar way a family of A_{2n−1} ^{(2)} integrable open spin chains with U_{q}(D_{n}) symmetry, and two families of D_{n+1} ^{(2)} integrable open spin chains with U_{q}(B_{n}) 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 D_{n+1} ^{(2)} chains with other integrable boundary conditions, which do not have quantum group symmetry.

Original language | English (US) |
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Pages (from-to) | 86-127 |

Number of pages | 42 |

Journal | Nuclear Physics B |

Volume | 924 |

DOIs | |

State | Published - Nov 1 2017 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

_{2n−1}

^{(2)}and D

_{n+1}

^{(2)}open spin chains.

*Nuclear Physics B*,

*924*, 86-127. https://doi.org/10.1016/j.nuclphysb.2017.09.004