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Greiter M. Mapping of Parent Hamiltonians. From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains

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Greiter M. Mapping of Parent Hamiltonians. From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains
Springer-Verlag Berlin Heidelberg, 2011. — 194 p. — (Springer Tracts in Modern Physics 244). — ISBN: 978-3-642-24384-4 (eBook), 978-3-642-43782-3 (Softcover), 978-3-642-24383-7 (Hardcover).
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.
Contents:
Introduction and Summary.
Three Models and a Ground State.
From a Laughlin State to the Haldane–Shastry Model.
From a Bosonic Pfaffian State to an.
Generalization to Arbitrary Spin.
Conclusions and Unresolved Issues.
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