### Abstract

Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras gˆ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the pth node from the gˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.

Original language | English (US) |
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Pages (from-to) | 266-297 |

Number of pages | 32 |

Journal | Nuclear Physics B |

Volume | 938 |

DOIs | |

State | Published - Jan 1 2019 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*938*, 266-297. https://doi.org/10.1016/j.nuclphysb.2018.11.017

**The spectrum of quantum-group-invariant transfer matrices.** / Nepomechie, Rafael; Retore, Ana L.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 938, pp. 266-297. https://doi.org/10.1016/j.nuclphysb.2018.11.017

}

TY - JOUR

T1 - The spectrum of quantum-group-invariant transfer matrices

AU - Nepomechie, Rafael

AU - Retore, Ana L.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras gˆ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the pth node from the gˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.

AB - Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras gˆ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the pth node from the gˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.

UR - http://www.scopus.com/inward/record.url?scp=85057181774&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057181774&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2018.11.017

DO - 10.1016/j.nuclphysb.2018.11.017

M3 - Article

VL - 938

SP - 266

EP - 297

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -