Using a high-accuracy variational Monte Carlo approach based on group-convolutional neural networks, we obtain the symmetry-resolved low-energy spectrum of the spin-$1/2$ Heisenberg model on several highly symmetric fullerene geometries, including the famous ${\mathrm{C}}_{60}$ 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 organized 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.

• Received 21 November 2023
• Accepted 3 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.054410

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society