Frustrated magnetism and resonating valence bond physics in 2D kagome-like magnets with inequivalent loops

Using a combination of exact diagonalization, analytical strong-coupling theories and resonating valence bond approaches we determine the phase diagram and the low-energy physics of three kagome-like Heisenberg antiferromagnets with inequivalent resonance loops. At weak coupling the lattices become effectively bipartite, while at strong coupling heavily frustrated nets emerge. Competing tunneling amplitudes result in the intermediate coupling regime in short-ranged spin correlations, the presence of a manyfold of low-lying singlets and the stabilization of valence bond crystal and spin-nematic phases.