Conformal Nature of Quantum Phase Transitions via Fuzzy Three-Sphere Regularization

Xue Meng; Liangdong Hu; Wei Zhu

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arXiv · 2607.11371

Conformal Nature of Quantum Phase Transitions via Fuzzy Three-Sphere Regularization

Xue Meng·Liangdong Hu·Wei Zhu

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Abstract

Conformal field theory (CFT) offers a modern viewpoint for understanding phase transitions. However, directly accessing the conformal algebra and microscopically uncovering the emergent conformal symmetry, especially in higher dimensions, remains a significant challenge. Motivated by recent advances in revealing CFT features via the fuzzy two-sphere, here we generalize this approach to higher dimensions and aim to expose the conformality at the (3+1)-D quantum critical point. We demonstrate this framework by investigating quantum phase transitions belonging to the Ising and Yang-Lee universality classes in a (3+1)-D quantum model (equivalent to a classical four-dimensional system), realized via Landau level projection on the fuzzy three-sphere. By computing the energy spectra at criticality, we explicitly verify the state-operator correspondence, a hallmark of conformal invariance. Together with prior advances, this work establishes a new pathway for the microscopic study of emergent conformality in higher-dimensional phase transitions.

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Xue Meng, Liangdong Hu, Wei Zhu. 2026-07-13. Conformal Nature of Quantum Phase Transitions via Fuzzy Three-Sphere Regularization. https://arxiv.org/abs/2607.11371

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