Mapping of Parent Hamiltonians

From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains

Nonfiction, Science & Nature, Science, Physics, Solid State Physics, Quantum Theory
Cover of the book Mapping of Parent Hamiltonians by Martin Greiter, Springer Berlin Heidelberg
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Author: Martin Greiter ISBN: 9783642243844
Publisher: Springer Berlin Heidelberg Publication: December 4, 2011
Imprint: Springer Language: English
Author: Martin Greiter
ISBN: 9783642243844
Publisher: Springer Berlin Heidelberg
Publication: December 4, 2011
Imprint: Springer
Language: English

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.

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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.

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