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

2009/11/30 by Rafael I. Nepomechie
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Bethe ansatz #Black Holes and Theoretical Physics #Boundary (topology) #Combinatorics #Generalization #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2010.01.006

27 pages; v2: minor change; v3: references added

arxiv created 2010/01/08 · openalex publication_date 2010/01/15 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider an open spin chain model with GL(N) bulk symmetry that is broken to GL(M) x 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.

Citations

• Magic in the spectra of the XXZ quantum chain with boundaries at Δ=0 and Δ=−1/2
• General boundary conditions for the and open spin chains
• The two-boundary Temperley–Lieb algebra
• New solutions to the reflection equation and the projecting method
• Boundary operators in theO(n) and RSOS matrix models
• Integrable Kondo impurities in one-dimensional extended Hubbard models
• Boundary conditions for integrable quantum systems
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries