Generalized hard-core dimer model approach to low-energy Heisenberg frustrated antiferromagnets: General properties and application to the kagome antiferromagnet

We propose a general nonperturbative scheme that quantitatively maps the low-energy sector of spin-1/2 frustrated Heisenberg antiferromagnets to effective generalized quantum dimer models. We develop the formal lattice-independent frame and establish some important results on (i) the locality of the generated Hamiltonians, (ii) how full resummations can be performed in this renormalization scheme. The method is then applied to the much debated kagome antiferromagnet for which a fully resummed effective Hamiltonian---shown to capture the essential properties and provide deep insights on the microscopic model [D. Poilblanc, M. Mambrini, and D. Schwandt, Phys. Rev. B 81, 180402(R) (2010)]---is derived.