Mapping of Parent Hamiltonians

Beschreibung

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.
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.
Integrates classic material and new concepts Presents precise and reproducible accounts of model discovery Inspires students and researchers to further advances in this field Includes supplementary material: sn.pub/extras

Autor*in

Martin Greiter

Themen in »Mapping of Parent Hamiltonians«

Abelian and non-Abelian statistics Critical model Exact models Haldane-Shastry Model Integrable models Laughlin state Pfaffian state Quantum Hall states Spin chains Wess-Zumino Witten model

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