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

Hamiltonian systems --- Quantum Hall effect --- Spin excitations --- Geometric quantization --- Mappings (Mathematics) --- Non-Abelian groups --- Particles (Nuclear physics) --- Mathematical physics --- Physics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Atomic Physics --- Applied Physics --- Mathematical models --- Physical mathematics --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Groups, Non-Abelian --- Groups, Nonabelian --- Nonabelian groups --- Maps (Mathematics) --- Geometry, Quantum --- Quantization, Geometric --- Quantum geometry --- Excitations, Spin --- Quantised Hall effect --- Quantized Hall effect --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Mathematics --- Physics. --- Mathematical physics. --- Quantum physics. --- Solid state physics. --- Statistical physics. --- Dynamical systems. --- Quantum Physics. --- Solid State Physics. --- Statistical Physics, Dynamical Systems and Complexity. --- Mathematical Methods in Physics. --- Mathematical Physics. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Mathematical statistics --- Solids --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Thermodynamics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Statistical methods --- Quantum theory. --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Hamiltonian systems. --- Geometric quantization. --- Non-Abelian groups. --- Mathematical models. --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- Geometry, Differential --- Quantum theory --- Nuclear excitation --- Nuclear spin --- Nuclear physics --- Group theory --- Hall effect --- Differentiable dynamical systems