Bulk and Boundary S Matrices for the SU (N ) Chain
نویسندگان
چکیده
We consider both closed and open integrable antiferromagnetic chains constructed with the SU(N )-invariant R matrix. For the closed chain, we extend the analyses of Sutherland and Kulish – Reshetikhin by considering also complex “string” solutions of the Bethe Ansatz equations. Such solutions are essential to describe general multiparticle excited states. We also explicitly determine the SU(N ) quantum numbers of the states. In particular, the model has particle-like excitations in the fundamental representations [k] of SU(N ), with k = 1 , . . . ,N − 1. We directly compute the complete two-particle S matrices for the cases [1] ⊗ [1] and [1] ⊗ [N − 1]. For the open chain with diagonal boundary fields, we show that the transfer matrix has the symmetry SU(l)×SU(N − l)×U(1), as well as a new “duality” symmetry which maps l ↔ N − l. With the help of these symmetries, we compute by means of the Bethe Ansatz for particles of types [1] and [N − 1] the corresponding boundary S matrices.
منابع مشابه
Boundary scattering in the SU(N) principal chiral model on the half-line with conjugating boundary conditions
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