00000cmm a22000004a 4500 UP-99796217611272853 Buklod 20241021165716.0 m go j cr |n |||auu|a 241021s2011 gw o j eng d 9783642243844 (eBook) (iLib)UPD-00216804759 DMLR rda eng DMLUC QC 20.7 H35 G74 2011eb Greiter, Martin. author. Mapping of parent Hamiltonians from Abelian and non-Abelian quantum hall states to exact models of critical spin chains [electronic resource] Martin Greiter. Heidelberg, Germany Springer Berlin 2011. 1 online resource (xiv, 194 pages) illustrations. text rdacontent computer rdamedia online resource rdacarrier Springer tracts in modern physics Volume 244. 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. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. 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 S1/2.  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 mec Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through Spring Hamiltonian systems. Mathematical physics . Quantum Hall effect Mathematical models . Available for UP System via Springer Link. https://doi.org/10.1007/978-3-642-24384-4 FO UPD DMLR QC 20.7 H35 G74 2011eb Electronic Resource