We examine a simple heuristic test of integrability for quantum chains. This test is applied to a variety of systems, including isotropic spin-1 models with nearest-neighbour interaction, Potts-type, inhomogeneous spin- 1/2 chains, and a multiparameter family of spin- 1/2 models generalizing the XYZ chain, with next-to-nearest neighbour interactions and bond alternation. Within the latter family we determine all the integrable models with an o(2) symmetry.
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Grabowski et al. (1995) studied this question.
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