### Abstract

For generic values of q, all the eigenvectors of the transfer matrix of the Uqsl(2)-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q is a root of unity ([Formula presented] with integer [Formula presented]), the Bethe equations acquire continuous solutions, and the transfer matrix develops Jordan cells. Hence, there appear eigenvectors of two new types: eigenvectors corresponding to continuous solutions (exact complete p-strings), and generalized eigenvectors. We propose general ABA constructions for these two new types of eigenvectors. We present many explicit examples, and we construct complete sets of (generalized) eigenvectors for various values of p and N.

Original language | English (US) |
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Pages (from-to) | 796-839 |

Number of pages | 44 |

Journal | Nuclear Physics B |

Volume | 909 |

DOIs | |

State | Published - Aug 1 2016 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*909*, 796-839. https://doi.org/10.1016/j.nuclphysb.2016.06.007

**Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity.** / Gainutdinov, Azat M.; Nepomechie, Rafael.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 909, pp. 796-839. https://doi.org/10.1016/j.nuclphysb.2016.06.007

}

TY - JOUR

T1 - Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity

AU - Gainutdinov, Azat M.

AU - Nepomechie, Rafael

PY - 2016/8/1

Y1 - 2016/8/1

N2 - For generic values of q, all the eigenvectors of the transfer matrix of the Uqsl(2)-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q is a root of unity ([Formula presented] with integer [Formula presented]), the Bethe equations acquire continuous solutions, and the transfer matrix develops Jordan cells. Hence, there appear eigenvectors of two new types: eigenvectors corresponding to continuous solutions (exact complete p-strings), and generalized eigenvectors. We propose general ABA constructions for these two new types of eigenvectors. We present many explicit examples, and we construct complete sets of (generalized) eigenvectors for various values of p and N.

AB - For generic values of q, all the eigenvectors of the transfer matrix of the Uqsl(2)-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q is a root of unity ([Formula presented] with integer [Formula presented]), the Bethe equations acquire continuous solutions, and the transfer matrix develops Jordan cells. Hence, there appear eigenvectors of two new types: eigenvectors corresponding to continuous solutions (exact complete p-strings), and generalized eigenvectors. We propose general ABA constructions for these two new types of eigenvectors. We present many explicit examples, and we construct complete sets of (generalized) eigenvectors for various values of p and N.

UR - http://www.scopus.com/inward/record.url?scp=84975295231&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975295231&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2016.06.007

DO - 10.1016/j.nuclphysb.2016.06.007

M3 - Article

AN - SCOPUS:84975295231

VL - 909

SP - 796

EP - 839

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -