Mapping of Parent Hamiltonians [recurso electrónico] : From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains / by Martin Greiter.

Por: Greiter, Martin [author.]Colaborador(es): SpringerLink (Online service)Tipo de material: TextoTextoSeries Springer Tracts in Modern Physics ; 244Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Descripción: XIV, 194 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642243844Tema(s): Physics | Quantum theory | Mathematical physics | Physics | Condensed Matter Physics | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Methods in Physics | Mathematical PhysicsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 530.41 Clasificación LoC:QC173.45-173.458Recursos en línea: Libro electrónicoTexto
Contenidos:
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 S = 1 spin chain -- Generalization to arbitrary spin S -- Conclusions and unresolved issues -- Spherical coordinates -- Fourier sums for one-dimensional lattices -- Angular momentum algebra -- Tensor decompositions of spin operators.
En: Springer eBooksResumen: 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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Libro Electrónico Biblioteca Electrónica
Colección de Libros Electrónicos QC173.45 -173.458 (Browse shelf(Abre debajo)) 1 No para préstamo 376779-2001

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 S = 1 spin chain -- Generalization to arbitrary spin S -- Conclusions and unresolved issues -- Spherical coordinates -- Fourier sums for one-dimensional lattices -- Angular momentum algebra -- Tensor decompositions of spin operators.

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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