TY - BOOK ID - 7913971 TI - Mapping of Parent Hamiltonians : From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains PY - 2011 SN - 3642243835 3642243843 PB - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, DB - UniCat KW - Hamiltonian systems KW - Quantum Hall effect KW - Spin excitations KW - Geometric quantization KW - Mappings (Mathematics) KW - Non-Abelian groups KW - Particles (Nuclear physics) KW - Mathematical physics KW - Physics KW - Engineering & Applied Sciences KW - Physical Sciences & Mathematics KW - Atomic Physics KW - Applied Physics KW - Mathematical models KW - Physical mathematics KW - Elementary particles (Physics) KW - High energy physics KW - Nuclear particles KW - Nucleons KW - Groups, Non-Abelian KW - Groups, Nonabelian KW - Nonabelian groups KW - Maps (Mathematics) KW - Geometry, Quantum KW - Quantization, Geometric KW - Quantum geometry KW - Excitations, Spin KW - Quantised Hall effect KW - Quantized Hall effect KW - Hamiltonian dynamical systems KW - Systems, Hamiltonian KW - Mathematics KW - Physics. KW - Mathematical physics. KW - Quantum physics. KW - Solid state physics. KW - Statistical physics. KW - Dynamical systems. KW - Quantum Physics. KW - Solid State Physics. KW - Statistical Physics, Dynamical Systems and Complexity. KW - Mathematical Methods in Physics. KW - Mathematical Physics. KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Statics KW - Mathematical statistics KW - Solids KW - Quantum dynamics KW - Quantum mechanics KW - Quantum physics KW - Thermodynamics KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics KW - Statistical methods KW - Quantum theory. KW - Complex Systems. KW - Statistical Physics and Dynamical Systems. KW - Hamiltonian systems. KW - Geometric quantization. KW - Non-Abelian groups. KW - Mathematical models. KW - Functions KW - Functions, Continuous KW - Topology KW - Transformations (Mathematics) KW - Geometry, Differential KW - Quantum theory KW - Nuclear excitation KW - Nuclear spin KW - Nuclear physics KW - Group theory KW - Hall effect KW - Differentiable dynamical systems UR - https://www.unicat.be/uniCat?func=search&query=sysid:7913971 AB - 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. ER -