通过模糊三球面正则化研究量子相变的共形性质
Conformal Nature of Quantum Phase Transitions via Fuzzy Three-Sphere Regularization
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中文总结 AI 辅助
研究通过模糊二球面揭示共形场论特征的方法在高维的推广，以（3 + 1）维量子模型研究伊辛和杨 - 李普适类量子相变，计算临界能谱验证态 - 算符对应，为高维相变中涌现共形性的微观研究开辟新途径。
中文摘要 AI 辅助
共形场论为理解相变提供了现代视角。然而，直接获取共形代数并微观揭示涌现的共形对称性，尤其在高维中，仍是重大挑战。受通过模糊二球面揭示共形场论特征的最新进展启发，本文将此方法推广到高维，旨在揭示（3 + 1）维量子临界点的共形性。通过研究（3 + 1）维量子模型（等同于经典四维系统）中属于伊辛和杨 - 李普适类的量子相变来演示此框架，该模型通过在模糊三球面上的朗道能级投影实现。通过计算临界时的能谱，明确验证了态 - 算符对应，这是共形不变性的标志。这项工作与先前进展一起，为高维相变中涌现共形性的微观研究建立了新途径。
英文摘要
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.
