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Mapping of parent Hamiltonians : from Abelian and non-Abelian quantum Hall states to exact models of critical spin chains

Author: Martin Greiter
Publisher: Heidelberg ; New York : Springer, ©2011.
Series: Springer tracts in modern physics, 244.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"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  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Martin Greiter
ISBN: 9783642243837 3642243835
OCLC Number: 752068563
Description: xiv, 194 pages : illustrations ; 24 cm.
Contents: Introduction and Summary --
Three Models and a Ground State. The Laughlin State and Its Parent Hamiltonian ; The Haldane-Shastry Model ; The Moore-Read State and Its Parent Hamiltonian ; An S=1 Spin Liquid State Described by a Pfaffian. --
From a Laughlin State to the Haldane-Shastry Model. General Considerations ; Hilbert Space Renormalization ; Fourier Transformation ; The Defining Condition for the Gutzwiller State ; Rotations and Spherical Tensor Operators ; Construction of a Parent Hamiltonian for the Gutzwiller State ; The Rapidity Operator and More ; Concluding Remarks. --
From a Bosonic Pfaffian State to an S=1 Spin Chain. General Considerations ; Hilbert Space Renormalization ; Fourier Transformation ; The Defining Condition for the S=1 Pfaffian Chain ; Construction of a Parent Hamiltonian ; Vector Annihilation Operators ; Concluding Remarks. --
Generalization to Arbitrary Spin S.A Critical Spin Liquid State With Spin S ; The Defining Condition for the Spin S Chain ; Construction of a Parent Hamiltonian ; Vector Annihilation Operators ; Scalar Operators Constructed from Vectors ; The Case S = 1/2 Once More. --
Conclusions and Unresolved Issues.
Series Title: Springer tracts in modern physics, 244.
Responsibility: Martin Greiter.
More information:

Abstract:

Unlike the spinons in the Haldane-Shastry model, those proposed here obey non-abelian statistics and integrate classical and fresh concepts. The new model this volume introduces is derived by mapping  Read more...

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