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Recent numerical work (Nature 464, 847 (2010)) indicates the existence of a spin liquid phase (SL) that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice.
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Because the smallest ring exchange term involves six sites, we suspect that large energy differences are almost certainly robust against it. Small energy differences (as we find between different spin liquids) may be sensitive to its presence
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