Block spins and chirality in the frustrated Heisenberg model onkagome´ and triangular lattices

The spin-1/2 frustrated Heisenberg model (HM) is investigated using a block-spin perturbation approach on kagome$aai--- and triangular lattices. In both cases, after coarse graining the triangles on the original lattice and truncation of the Hilbert space to the triangular ground-state subspace, HM reduces to an effective model on a triangular lattice in terms of the triangular-block degrees of freedom, viz. the spin and the chirality quantum numbers. The chirality part of the effective Hamiltonian captures the essential difference between the two lattices. It is seen that chiral-ordered variational states have high energies compared to the other variational states.