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This monograph introduces an exact model for a critical spin chain witharbitrary spin S, which includes the Haldane--Shastry model as the special caseS=1/2. While spinons in the Haldane--Shastry model obey abelian half-fermistatistics, the spinons in the general model introduced here obey non-abelianstatistics. This manifests itself through topological choices for thefractional momentum spacings. The general model is derived by mapping exactmodels of quantized Hall states onto spin chains. The book begins withpedagogical review of all the relevant models including the non-abelianstatistics in the Pfaffian Hall state, and is understandable to every studentwith a graduate course in quantum mechanics.

Mapping of Parent Hamiltonians: from Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains