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

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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 languageEnglish (US)
Pages (from-to)429-451
Number of pages23
JournalNuclear Physics B
Volume831
Issue number3
DOIs
StatePublished - Jun 1 2010

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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