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The planar pyrochlore: a Valence Bond Crystal

J. -B. Fouet·M. Mambrini·P. Sindzingre·C. Lhuillier
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Abstract

Exact diagonalizations of the spin-1/2 Heisenberg model on the checkerboard lattice have been performed for sizes up to N=36 in the full Hilbert space and N=40 in the restricted subspace of first neighbor dimers. This antiferromagnet does not break SU(2) symmetry and displays long range order in 4-spin S=0 plaquettes. Both the symmetry properties of the spectrum and various correlations functions are extensively studied. At variance with the kagom{é} antiferromagnet, the Heisenberg quantum model on a checkerboard lattice is a Valence Bond Crystal. Some results concerning the 3-dimensionnal spin-1/2 pyrochlore magnet (for sizes 16 and 32) are also shown: this system could behave differently from its 2-dimensional analog.

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J. -B. Fouet, M. Mambrini, P. Sindzingre, C. Lhuillier. 2001-08-03. The planar pyrochlore: a Valence Bond Crystal. https://arxiv.org/abs/cond-mat/0108070

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