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Free real scalar CFT on fuzzy sphere: spectrum, algebra and wavefunction ansatz

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arxiv 2506.14904 v1 pith:JB37SOWO submitted 2025-06-17 hep-th cond-mat.stat-mechcond-mat.str-el

Yin-Chen He This is my paper
classification hep-thcond-mat.stat-mechcond-mat.str-el
keywords modelscalarfreefuzzyisingspherealgebraansatz
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abstract

We introduce a simple model to realize the free real scalar CFT on the fuzzy sphere. The model is structurally similar to the original model that realizes the 3D Ising CFT on the fuzzy sphere. Owing to the shift symmetry of the free scalar, the free scalar CFT fixed point in our model can be accessed with only a single tuning parameter-the conformal coupling. We numerically demonstrate that our model correctly reproduces the operator spectrum, correlation functions, and, crucially, the harmonic oscillator algebra of the real scalar CFT. We also examine the fuzzy sphere algebra, a generalization of the Girvin-MacDonald-Platzman algebra, and discuss its potential implications for defining quantum field theories on non-commutative geometries. Finally, we propose wavefunction ansatz for the ground states of both the free scalar and Ising CFTs, which exhibit remarkable agreement with the CFT ground state wavefunctions of the fuzzy sphere model. For instance, the wavefunction overlap between our Ising ansatz and the Ising CFT ground state exceeds $0.99$ for $N=28$ fermions, suggesting a promising direction for tackling the 3D Ising CFT.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Chern-Simons-matter conformal field theory on fuzzy sphere: Confinement transition of Kalmeyer-Laughlin chiral spin liquid

    cond-mat.str-el 2025-07 conditional novelty 8.0 of 10

    A fuzzy-sphere exact diagonalization study shows the fIQH to bFQH transition is continuous, with emergent conformal symmetry and a single relevant singlet of scaling dimension Delta_S = 1.52(18).

  2. Conformal scalar field theory from Ising tricriticality on the fuzzy sphere

    cond-mat.str-el 2025-06 conditional novelty 7.0 of 10

    A bilayer quantum Hall fuzzy-sphere model, tuned to an Ising tricritical point, realizes the conformally coupled free scalar CFT, verified by matching spectra, operator content, and bosonic algebra.

  3. 3d Conformal Field Theories via Fuzzy Sphere Algebra

    cond-mat.str-el 2026-02 conditional novelty 6.0 of 10

    The fuzzy-sphere density-mode algebra is a genuine Lie algebra, but a direct density-mode realization of the 3d conformal algebra so(3,2) exists only for the two-electron system.

  4. The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere

    cond-mat.str-el 2025-12 conditional novelty 5.0 of 10

    Fuzzy-sphere Hamiltonians realize the O(2), O(3) and O(4) Wilson-Fisher and free-scalar CFTs numerically, with spectra and correlators matching conformal bootstrap expectations.

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