Correlations for the S=1/2 Antiferromagnet on a Truncated Tetrahedron

Abstract

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 $C_{60}$. We study 2- and 4-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 wavefunction based on the classical ground state. This suggests that the correlations present in the classical ground state of $C_{60}$ also survive in the exact ground state of that system, for a range of bond strengths about the physically relevant $J_2\approx J_1$. We calculate the momentum-space correlation function $S(q)$, which is measurable by neutron scattering, for both $C_{12}$ and $C_{60}$. We also calculate correlations at finite temperature.

17 pages, 6 figures. (Figure 1 included, others available on request from the authors.)

References in corpus (1)

• Magnetic Properties of Undoped $C_{60}$

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