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A class of local SU(2)-invariant spin-1/2 Hamiltonians is studied that hasground states within the space of nearest neighbor valence bond states on thekagome lattice. Cases include "generalized Klein'' models without obviousnon-valence bond ground states, as well as a "resonating-valence-bond"Hamiltonian whose unique ground states within the nearest neighbor valence bondspace are four topologically degenerate "Sutherland-Rokhsar-Kivelson'' (SRK)type wavefunctions, which are expected to describe a gapped $\mathbb{Z}_2$ spinliquid. The proof of this uniqueness is intimately related to the linearindependence of the nearest neighbor valence bond states on quite general andarbitrarily large kagome lattices, which is also established in this work. Itis argued that the SRK ground states are also unique within the entire Hilbertspace, depending on properties of the generalized Klein models. Applications ofthe strategies developed in this work to other lattice types are alsodiscussed.

physical review. b, condensed matter and materials physics

Linear independence of nearest neighbor valence bond states on the  kagome lattice and construction of SU(2)-invariant spin-1/2-Hamiltonian with  a Sutherland-Rokhsar-Kivelson quantum liquid ground state