### Abstract

Using anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A_{2n} ^{(2)}, A_{2n−1} ^{(2)}, B_{n} ^{(1)}, C_{n} ^{(1)}, D_{n} ^{(1)}) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. We show that these transfer matrices also have a duality symmetry (for the cases C_{n} ^{(1)} and D_{n} ^{(1)}) and additional Z_{2} symmetries that map complex representations to their conjugates (for the cases A_{2n−1} ^{(2)}, B_{n} ^{(1)} and D_{n} ^{(1)}). A key simplification is achieved by working in a certain “unitary” gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.

Original language | English (US) |
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Pages (from-to) | 91-134 |

Number of pages | 44 |

Journal | Nuclear Physics B |

Volume | 930 |

DOIs | |

State | Published - May 1 2018 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*930*, 91-134. https://doi.org/10.1016/j.nuclphysb.2018.02.023

**Surveying the quantum group symmetries of integrable open spin chains.** / Nepomechie, Rafael; Retore, Ana L.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 930, pp. 91-134. https://doi.org/10.1016/j.nuclphysb.2018.02.023

}

TY - JOUR

T1 - Surveying the quantum group symmetries of integrable open spin chains

AU - Nepomechie, Rafael

AU - Retore, Ana L.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - Using anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A2n (2), A2n−1 (2), Bn (1), Cn (1), Dn (1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. We show that these transfer matrices also have a duality symmetry (for the cases Cn (1) and Dn (1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n−1 (2), Bn (1) and Dn (1)). A key simplification is achieved by working in a certain “unitary” gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.

AB - Using anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A2n (2), A2n−1 (2), Bn (1), Cn (1), Dn (1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. We show that these transfer matrices also have a duality symmetry (for the cases Cn (1) and Dn (1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n−1 (2), Bn (1) and Dn (1)). A key simplification is achieved by working in a certain “unitary” gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.

UR - http://www.scopus.com/inward/record.url?scp=85042909214&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042909214&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2018.02.023

DO - 10.1016/j.nuclphysb.2018.02.023

M3 - Article

AN - SCOPUS:85042909214

VL - 930

SP - 91

EP - 134

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -