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Valence bond ground states in isotropic quantum antiferromagnets

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Abstract

Haldane predicted that the isotropic quantum Heisenberg spin chain is in a “massive” phase if the spin is integral. The first rigorous example of an isotropic model in such a phase is presented. The Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but we prove the model has a unique ground state, a gap in the spectrum of the Hamiltonian immediately above the ground state and exponential decay of the correlation functions in the ground state. Models in two and higher dimension which are expected to have the same properties are also presented. For these models we construct an exact ground state, and for some of them we prove that the two-point function decays exponentially in this ground state. In all these models exact ground states are constructed by using valence bonds.

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Authors and Affiliations

  1. Department of Physics, University of British Columbia, V6T2A6, Vancouver, B.C., Canada

    Ian Affleck

  2. Department of Physics, Princeton University, P.O. Box 708, 08544, Princeton, NJ, USA

    Tom Kennedy, Elliott H. Lieb & Hal Tasaki

Authors
  1. Ian Affleck
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  2. Tom Kennedy
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  3. Elliott H. Lieb
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  4. Hal Tasaki
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Additional information

Communicated by A. Jaffe

Supported in part by N.S.F. Grant PHY-80-19754. Fellow of the A.P. Sloan Foundation and the Canadian Institute for Advanced Research

N.S.F. Post-doctoral Fellow

Supported in part by N.S.F. Grant PHY-85-15288-A01

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Affleck, I., Kennedy, T., Lieb, E.H. et al. Valence bond ground states in isotropic quantum antiferromagnets. Commun.Math. Phys. 115, 477–528 (1988). https://doi.org/10.1007/BF01218021

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  • DOI: https://doi.org/10.1007/BF01218021

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