Joint Condensed Matter Theory and Particle Theory Seminar - Zheng Zhou - Harvard University

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Advancing Fuzzy-Sphere CFTs: Heavy Primaries and Hilbert-Space Structure

Fuzzy-sphere regularization has emerged as a powerful framework for studying three-dimensional conformal field theories (CFTs). Heavy operators represent a compelling frontier, with connections to quantum chaos, thermalization, and holography that motivate a deeper understanding of their spectrum and structure. However, accessing these operators remains challenging even with the fuzzy-sphere. We address this challenge by developing an exact-diagonalization algorithm that resolves the full SO(3) rotational symmetry. For the 3D Ising CFT, we identify approximately 100 primary operators, including many previously unknown heavy scalar primaries with scaling dimensions up to Δ ≈ 16.5. Within the scalar primaries, we identify a branch associated with ϕ^n operators in the ϕ^4 Lagrangian description, beginning with σ, ϵ, ϵ', and σ'. Their wave functions exhibit a semi-classical structure closely related to the area-preserving diffeomorphism. Finally, we show that critical points involving fractional quantum Hall states can be studied in a substantially reduced Hilbert space spanned by quasi-hole states of the corresponding FQH wave functions. This suggests a general strategy for exploring CFTs intertwined with topologically ordered phases. This talk is based on arXiv:2609.35960.

Biography: Zheng Zhou (周正) is a post-doctoral fellow at Harvard University, Department of Physics. He received his Ph. D. at Perimeter Institute for Theoretical Physics in 2026. His research focuses on quantum many-body physics and critical behaviour, especially conformal field theories.

Hosts: Meng Cheng and Ian Moult