Correlations for theS=1/2 antiferromagnet on a truncated tetrahedron

The antiferromagnetic Heisenberg Hamiltonian is investigated on a truncated tetrahedron, which is a closed 12-site system. We find that the ground state has many similarities to that of C₆₀. We study two- and four-spin correlations in the classical ground state of the truncated tetrahedron and calculate the same correlations in the exact S=1/2 ground state. We find that the classical correlations survive for a range of bond strengths in the Heisenberg Hamiltonian and that one can construct a good trial wave function based on the classical ground state. This suggests that the correlations present in the classical ground state of C₆₀ also survive in the exact ground state of that system, for a range of bond strengths about the physically relevant J₂{}J₁. We calculate the momentum-space correlation function S(q), which is measurable by neutron scattering, for both C₁₂ and C₆₀. We also calculate correlations at finite temperature.