A family of spin-S chain representations of SU(2)_k Wess-Zumino-Witten models

Abstract

We investigate a family of spin-S chain Hamiltonians recently introduced by one of us. For S=1/2, it corresponds to the Haldane-Shastry model. For general spin S, we find indication that the low-energy theory of these spin chains is described by the SU(2)_k Wess-Zumino-Witten model with coupling k=2S. In particular, we investigate the S=1 model whose ground state is given by a Pfaffian for even number of sites N. We reconcile aspects of the spectrum of the Hamiltonian for arbitrary N with trial states obtained by Schwinger projection of two Haldane-Shastry chains.

arXiv comment4.3 pages, 4 figures

References in corpus (8)

• Entanglement Entropy and Quantum Field Theory
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Quantum spin Hamiltonians for the SU(2)_k WZW model
• DMRG studies of critical SU(N) spin chains
• Spinon confinement and the Haldane gap in SU(n) spin chains
• Mapping of Parent Hamiltonians: from Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains

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