The $s=1/2$ Antiferromagnetic Heisenberg Model on Fullerene-Type Symmetry Clusters

TL;DR

This study investigates the low-energy spectrum and magnetic properties of the spin-1/2 antiferromagnetic Heisenberg model on fullerene-like clusters, revealing the influence of symmetry and frustration on their quantum states.

Contribution

It provides a comprehensive analysis of the low-energy states and magnetic behavior of fullerene-type clusters, highlighting the role of symmetry and connectivity in these quantum systems.

Findings

Lowest excited states are singlets except for n=28.

Magnetization shows plateaux, with the most pronounced at n=28.

Spatial symmetry and connectivity significantly affect magnetic properties.

Abstract

The $s_{i}={1/2}$ nearest neighbor antiferromagnetic Heisenberg model is considered for spins sitting on the vertices of clusters with the connectivity of fullerene molecules and a number of sites $n$ ranging from 24 to 32. Using the permutational and spin inversion symmetries of the Hamiltonian the low energy spectrum is calculated for all the irreducible representations of the symmetry group of each cluster. Frustration and connectivity result in non-trivial low energy properties, with the lowest excited states being singlets except for $n=28$. Same hexagon and same pentagon correlations are the most effective in the minimization of the energy, with the $n=32-D_{3h}$ symmetry cluster having an unusually strong singlet intra-pentagon correlation. The magnetization in a field shows no discontinuities unlike the icosahedral $I_h$ fullerene clusters, but only plateaux with the most pronounced for $n=28$. The spatial symmetry as well as the connectivity of the clusters appear to be important for the determination of their magnetic properties.