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

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arxiv 2510.09755 v3 pith:YOCFNECU submitted 2025-10-10 cond-mat.str-el hep-th

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

Arjun Dey , Loic Herviou , Christopher Mudry , Andreas Martin L\"auchli This is my paper
classification cond-mat.str-el hep-th
keywords conformalfuzzyquantumspheretheorydatafieldmodel
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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).

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Cited by 5 Pith papers

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  1. Quantum Rotors on the Fuzzy Sphere and the Cubic CFT

    cond-mat.str-el 2026-04 conditional novelty 7.0

    Adding a cubic two-body interaction to quantum rotors on the fuzzy sphere isolates the cubic CFT critical point, enabling calculation of scaling dimensions for key operators that match existing benchmarks.

  2. Studying 3D O(N) Surface CFT on the Fuzzy Sphere

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    Boundary CFT spectra, OPE coefficients, and central charges are extracted for normal and ordinary boundaries of the 3D O(2) and O(3) Wilson-Fisher fixed points via fuzzy-sphere state-operator correspondence, with conf...

  3. Fortuitous Universality of Bose-Kondo Impurities

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  4. Conformal Data for the $O(2)$ Wilson-Fisher CFT in $(2+1)$-Dimensional Spacetime from Exact Diagonalization and Matrix Product States on the Fuzzy Sphere

    cond-mat.str-el 2026-04 unverdicted novelty 6.0

    Numerical extraction of scaling dimensions and OPE coefficients for 32 primary operators in the O(2) Wilson-Fisher CFT via fuzzy-sphere regularization shows agreement with bootstrap predictions.

  5. Toward Entanglement Bootstrap for Conformal Field Theory in Any Dimension

    hep-th 2026-06 unverdicted novelty 5.0

    Proposes and numerically tests a reconstructed Hamiltonian for approximate CFT ground states in any dimension that recovers CFT spectral properties.