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Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet

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Abstract

We study a class of two-dimensional spin-1/2 Heisenberg antiferromagnets, introduced by Klein [1], in which the nearest-neighbor term is supplemented by next-nearest-neighbor pair and four-body interactions, producing additional frustration. For certain lattices, including e.g. the hexagonal lattice, we prove that any finite subset which admits a dimer covering has a ground state space spanned by valence bond states, each of which consists only of nearest-neighbor (dimer) singlet pairs. We also establish linear independence of these valence bond states. The possible relevance to resonating-valence-bond theories of high-temperature superconductors is briefly discussed. In particular, our results apply both to regular subsets of the lattice and to subsets with static holes.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 90024, Los Angeles, California, USA

    J. T. Chayes & L. Chayes

  2. Department of Physics, SUNY at Stony Brook, 11794, Stony Brook, New York, USA

    S. A. Kivelson

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  1. J. T. Chayes
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  2. L. Chayes
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  3. S. A. Kivelson
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Communicated by A. Jaffe

Work supported in part by N.S.F. Postdoctoral Research Fellowships

Work supported by N.S.F. Grant No. DMR-83-18051

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Chayes, J.T., Chayes, L. & Kivelson, S.A. Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet. Commun.Math. Phys. 123, 53–83 (1989). https://doi.org/10.1007/BF01244017

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  • DOI: https://doi.org/10.1007/BF01244017

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