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Quantum rotors on the fuzzy sphere and the cubic conformal field theory

Andreas Stergiou

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Phys. Rev. B 114, 225103 – Published 2 October, 2026

DOI: https://doi.org/10.1103/l56l-7sp6

Abstract

The three-dimensional cubic conformal field theory governs the critical behavior of Heisenberg magnets with cubic anisotropy. Studying this theory nonperturbatively 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 regularization 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 diagonalization and the density matrix renormalization 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 Eg and T2g representations of the cubic group. Our results are consistent with existing Monte Carlo, conformal perturbation theory, and ɛ expansion benchmarks, demonstrating the power of the fuzzy sphere in resolving closely spaced universality classes.

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Phys. Rev. B 114, 225103– Published 2 October, 2026
  • Received 21 May 2026
  • Revised 2 August 2026
  • Accepted 21 September 2026
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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.

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