### Abstract

We consider an open spin chain model with GL (N) bulk symmetry that is broken to GL (M) × GL (N - M) by the boundary, which is a generalization of a model arising in string/gauge theory. We prove the integrability of this model by constructing the corresponding commuting transfer matrix. This construction uses operator-valued "projected" K-matrices. We solve this model for general values of N and M using the nested algebraic Bethe ansatz approach, despite the fact that the K-matrices are not diagonal. The key to obtaining this solution is an identity based on a certain factorization property of the reduced K-matrices into products of R-matrices. Numerical evidence suggests that the solution is complete.

Original language | English (US) |
---|---|

Pages (from-to) | 429-451 |

Number of pages | 23 |

Journal | Nuclear Physics B |

Volume | 831 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2010 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Nested algebraic Bethe ansatz for open GL (N) spin chains with projected K-matrices.** / Nepomechie, Rafael.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 831, no. 3, pp. 429-451. https://doi.org/10.1016/j.nuclphysb.2010.01.006

}

TY - JOUR

T1 - Nested algebraic Bethe ansatz for open GL (N) spin chains with projected K-matrices

AU - Nepomechie, Rafael

PY - 2010/6/1

Y1 - 2010/6/1

N2 - We consider an open spin chain model with GL (N) bulk symmetry that is broken to GL (M) × GL (N - M) by the boundary, which is a generalization of a model arising in string/gauge theory. We prove the integrability of this model by constructing the corresponding commuting transfer matrix. This construction uses operator-valued "projected" K-matrices. We solve this model for general values of N and M using the nested algebraic Bethe ansatz approach, despite the fact that the K-matrices are not diagonal. The key to obtaining this solution is an identity based on a certain factorization property of the reduced K-matrices into products of R-matrices. Numerical evidence suggests that the solution is complete.

AB - We consider an open spin chain model with GL (N) bulk symmetry that is broken to GL (M) × GL (N - M) by the boundary, which is a generalization of a model arising in string/gauge theory. We prove the integrability of this model by constructing the corresponding commuting transfer matrix. This construction uses operator-valued "projected" K-matrices. We solve this model for general values of N and M using the nested algebraic Bethe ansatz approach, despite the fact that the K-matrices are not diagonal. The key to obtaining this solution is an identity based on a certain factorization property of the reduced K-matrices into products of R-matrices. Numerical evidence suggests that the solution is complete.

UR - http://www.scopus.com/inward/record.url?scp=77249132245&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77249132245&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2010.01.006

DO - 10.1016/j.nuclphysb.2010.01.006

M3 - Article

AN - SCOPUS:77249132245

VL - 831

SP - 429

EP - 451

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -