Ground-state energy and spin gap of spin-12Kagomé-Heisenberg antiferromagnetic clusters: Large-scale exact diagonalization results
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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.
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