Static impurities in the $S=1/2\mathrm{}$ kagome lattice: Dimer freezing and mutual repulsion

We consider the effects of doping the $S=1/2\mathrm{}$ kagome lattice with static impurities. We demonstrate that impurities lower the number of low-lying singlet states, induce dimer-dimer correlations of considerable spatial extent, and do not generate free spin degrees of freedom. Most importantly, they experience a highly unconventional mutual repulsion as a direct consequence of the strong spin frustration. These properties are illustrated by exact diagonalization, and are reproduced to semiquantitative accuracy within a dimer resonating-valence-bond description which affords access to longer length scales. We calculate the local magnetization induced by doped impurities, and consider its implications for nuclear magnetic resonance measurements on known kagome systems.