Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions

Details Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions

2009-02-02

arxiv.org/abs/0902.0321v2

J. Phys. A42 (2009) 205203

Physics

Mathematical Physics

40 pages; examples of Bethe vectors added; Bethe equations for U_q(gl(2/2)) added; misprints corrected

Scientific paper

We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(\fn)), Y(gl(\fm|\fn)), U_{q}(gl(\fn)) or U_{q}(gl(\fm|\fn)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices (K^+(u),K^-(u)). The nested Bethe anstaz applies for a general K^-(u), but a particular form of the K^+(u) matrix. The construction extends and unifies the results already obtained for open spin chains based on fundamental representation and for some particular super-spin chains. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.

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