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Conformal Data for the O(3) Wilson-Fisher Conformal Field Theory from Fuzzy Sphere Realization of the Quantum Rotor Model

Arjun Dey1,2,*, Loic Herviou3, Christopher Mudry1,2, and Andreas Martin Läuchli1,2

  • *Contact author: arjundey123456789@gmail.com
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Phys. Rev. Lett. 136, 206504 – Published 21 May, 2026

DOI: https://doi.org/10.1103/4yfv-xbcj

Abstract

We present a model for strongly interacting fermions with internal O(3) symmetry on the fuzzy sphere that (i) preserves the rotational symmetry of the fuzzy sphere and (ii) undergoes a quantum phase transition in the (2+1)-dimensional O(3) Wilson-Fisher universality class. Using exact diagonalization and density matrix renormalization group, we locate the quantum critical point via conformal perturbation theory and obtain scaling dimensions from finite-size spectra. We identify 24 primary operators and determine some of their operator product expansion coefficients through first-order conformal perturbation theory. The results are benchmarked against conformal bootstrap and large quantum-number expansions and reveal a weakly irrelevant operator that plays a role in dimerized antiferromagnets. Our Letter provides a general framework for quantitatively accessing conformal data for O(N) Wilson-Fisher conformal field theories.

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Phys. Rev. Lett. 136, 206504– Published 21 May, 2026
  • Received 19 November 2025
  • Accepted 24 April 2026
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