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

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 (ED) and density matrix renormalization group (DMRG), 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 work establishes the fuzzy sphere as a general framework for quantitatively accessing conformal data in non-Abelian conformal field theories (CFTs).