Abstract
Quantum spin chains arise naturally from perturbative
large-N
field theories and matrix models. The Hamiltonian of such a model is a long-range
deformation of nearest-neighbour type interactions. Here, we study the most general
long-range integrable spin chain with spins transforming in the fundamental representation
of 
. We derive the Hamiltonian and the corresponding asymptotic Bethe ansatz at the
leading four perturbative orders with several free parameters. Furthermore, we propose
Bethe equations for all orders and identify the moduli of the integrable system. We finally
apply our results to plane-wave matrix theory and show that the Hamiltonian in a
closed sector is not of this form and therefore not integrable beyond the first
perturbative order. This also implies that the complete model is not integrable.
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A commentary on this article has been published by Sakura Schäfer-Nameki, 2006 J. Stat. Mech. N12001.