Quantum Rotors on the Fuzzy Sphere and the Cubic CFT

arXiv:2604.24840 · cond-mat.str-el, hep-th · Submitted 2026-04-27 · Read on arXiv

cond-mat.str-el, hep-th

Submitted: 2026-04-27

Updated: 2026-09-21

Comments: 24 pages, 6 figures, 4 tables. v2: minor revisions in response to referee reports; accepted for publication in Physical Review B. Code used in this work is available at https://github.com/andstergiou/fuzzy-cubic

License: http://creativecommons.org/licenses/by/4.0/

The gist: The three-dimensional cubic conformal field theory governs the critical behaviour of Heisenberg magnets with cubic anisotropy.

Terminology

Abstract

The three-dimensional cubic conformal field theory governs the critical behaviour of Heisenberg magnets with cubic anisotropy. Studying this theory non-perturbatively is challenging, because its most easily accessible observables are numerically very close to those of the more symmetric O(3) model. In this work, we overcome this difficulty using the fuzzy sphere regularisation method. By adding a cubic-invariant two-body interaction to the quantum rotor Hamiltonian used for the O(3) model, we break the continuous rotational symmetry by construction and unambiguously isolate the cubic critical point. Using exact diagonalisation and the density matrix renormalisation group, we calculate the scaling dimensions of several key operators, including the leading scalar singlets, and resolve the splitting of the O(3) rank-two traceless symmetric tensor into the E g and T 2g representations of the cubic group. Our results are consistent with existing Monte Carlo, conformal perturbation theory, and epsilon expansion benchmarks, demonstrating the power of the fuzzy sphere in resolving closely spaced universality classes.

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