Bulk and Boundary S Matrices for the SU(N) Chain

TL;DR

This paper analyzes the integrable SU(N) antiferromagnetic chain, extending Bethe Ansatz solutions to include complex string states, and explicitly computes bulk and boundary S matrices, revealing new symmetries and particle excitations.

Contribution

It extends Bethe Ansatz analysis to complex string solutions and explicitly derives bulk and boundary S matrices for SU(N) chains, revealing new symmetries.

Findings

Explicit two-particle S matrices for fundamental representations.

Identification of boundary symmetries including a duality.

Complete characterization of particle excitations and quantum numbers.

Abstract

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] X [1] and [1] X [N-1]. For the open chain with diagonal boundary fields, we show that the transfer matrix has the symmetry SU(l) X SU(N-l) X U(1), as well as a new ``duality'' symmetry which interchanges l and 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.