## Abstract

We present a nested algebraic Bethe ansatz for one-dimensional so
_{2n}- and sp
_{2n}-symmetric open spin chains with diagonal boundary conditions. The monodromy matrix of these spin chains satisfies the defining relations on the extended twisted Yangians X
_{ρ}(so
_{2n},so
_{2n}
^{ρ})
^{tw} and X
_{ρ}(sp
_{2n},sp
_{2n}
^{ρ})
^{tw}, respectively. We use a generalisation of the De Vega and Karowski approach allowing us to relate the spectral problem of so
_{2n}- or sp
_{2n}-symmetric open spin chain to that of gl
_{n}-symmetric open spin chain studied by Belliard and Ragoucy. We explicitly derive the structure of Bethe vectors, their eigenvalues and the nested Bethe equations. We also provide a proof of Belliard and Ragoucy's trace formula for Bethe vectors of gl
_{n}-symmetric open spin chains.

Original language | English |
---|---|

Article number | 114909 |

Pages (from-to) | 1-67 |

Number of pages | 67 |

Journal | Nuclear Physics B |

Volume | 952 |

Early online date | 2 Jan 2020 |

DOIs | |

Publication status | Published - 1 Mar 2020 |

## Keywords

- math-ph
- hep-th
- math.MP
- nlin.SI
- 82B23, 17B37