Ground state of the spin-1/2 Kagome antiferromagnet: A Contractor Renormalisation study

We study the low energy phase of the nearest neighbour spin-1/2 Kagome antiferromagnet using Contractor Renormalisation (CORE). The lattice is analysed as a triangular lattice of the 12 site "Star of David" clusters. The two degenerate singlet ground states of the star clusters define an effective spin-1/2 degree of freedom. We construct an effective Hamiltonian till the third order in the CORE expansion, whose accuracy is verified using a comparison with Density Matrix Renormalisation Group calculations. We find a ground state phase which is translationally invariant. However, the spectrum of the CORE effective Hamiltonian exhibits a near exact double degeneracy which signals the onset of p6 chirality symmetry breaking in the thermodynamic limit. This phase and the effective Hamiltonian is analysed using a mean field theory. Addition of small further neighbour interactions is discussed.