Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results

We present a comprehensive list of ground state energies and spin gaps of finite kagome clusters with up to 42 spins obtained using large-scale exact diagonalization techniques. This represents the current limit of this exact approach. For a fixed number of spins N we study several cluster shapes under periodic boundary conditions in both directions resulting in a toroidal geometry. The clusters are characterized by their side length and diagonal as well as the shortest "Manhattan" diameter of the torii. A finite-size scaling analysis of the ground state energy as well as the spin gap is then performed in terms of the shortest toroidal diameter as well as the shortest "Manhattan" diameter. The structure of the spin-spin correlations further supports the importance of short loops wrapping around the torii.