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Valence Bond Glass Phase in the Diluted Kagome Antiferromagnets

We present a theory for site dilution in the Valence Bond Crystal Phase of the Kagome Lattice Heisenberg Model. The presence of an empty site leads to strong singlet bond across the impurity. It also creates a free spin, which delocalizes inside the unit cell. Finite concentration of quenched impurities leads to a Valence Bond Glass phase. This phase has short-range Valence Bond order, no spin-gap, large spin susceptibilities, linear specific heat due to two-level systems, as well as singlet and triplet excitations that decompose into kink-antikink pairs delocalized over a few lattice constants. It provides a framework for a comprehensive understanding of thermodynamic, neutron, and Raman measurements in the Herbertsmithite material ZnCu3(OH)6Cl2, including recently reported H/T and omega/T scaling.