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

TL;DR

This paper investigates the ground state correlations of a spin-1/2 antiferromagnet on a truncated tetrahedron, revealing classical correlations persist in the quantum ground state and drawing parallels to the $C_{60}$ molecule.

Contribution

It demonstrates that classical correlations in a truncated tetrahedron model are retained in the quantum ground state, providing insights into the magnetic properties of similar molecular systems.

Findings

Classical correlations survive in the quantum ground state over a range of bond strengths.

A good trial wavefunction can be constructed from the classical ground state.

Calculated momentum-space correlations are relevant for neutron scattering experiments.

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.