  The doping of quantum Heisenberg antiferromagnets on the kagome lattice by
non-magnetic impurities is investigated within the framework of a generalized
quantum dimer model (QDM) describing a) the valence bond crystal (VBC), b) the
dimer liquid and c) the critical region on equal footing. Following the
approach by Ralko et al. [Phys. Rev. Lett. 101, 117204 (2008)] for the square
and triangular lattices, we introduce the (minimal) extension of the QDM on the
Kagome lattice to account for spontaneous creation of mobile S=1/2 spinons at
finite magnetic field. Modulations of the dimer density (at zero or finite
magnetic field) and of the local field-induced magnetization in the vicinity of
impurities are computed using Lanczos Exact Diagonalization techniques on small
clusters (48 and 75 sites). The VBC is clearly revealed from its pinning by
impurities, while, in the dimer liquid, crystallization around impurities
involves only two neighboring dimers. We also find that a next-nearest-neighbor
ferromagnetic coupling favors VBC order. Unexpectedly, a small size
spinon-impurity bound state appears in some region of the the dimer liquid
phase. In contrast, in the VBC phase the spinon delocalizes within a large
region around the impurity, revealing the weakness of the VBC confining
potential. Lastly, we observe that an impurity concentration as small as 4%
enhances dimerization substantially. These results are confronted to the
Valence Bond Glass scenario [R.R.P. Singh, Phys. Rev. Lett. 104, 177203 (2010)]
and implications to the interpretation of the Nuclear Magnetic Resonance
spectra of the Herbertsmithite compound are outlined.
