Noncoplanar and chiral spin states on the way towards Néel ordering in fullerene Heisenberg models

Using high-accuracy variational Monte Carlo based on group-convolutional neural networks (GCNNs), we obtain the symmetry-resolved low-energy spectrum of the spin-1/2 Heisenberg model on several highly symmetric fullerene geometries, including the famous C${}_{60}$ buckminsterfullerene. We argue that as the degree of frustration is lowered in large fullerenes, they display characteristic features of incipient magnetic ordering: correlation functions show high-intensity Bragg peaks consistent with Néel-like ordering, while the low-energy spectrum is organised into a tower of states. Competition with frustration, however, turns the simple Néel order into a noncoplanar one. Remarkably, we find and predict chiral incipient ordering in a large number of fullerene structures.