Conformal operator content of the Wilson-Fisher transition on fuzzy sphere bilayers,Physical Review B

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Conformal operator content of the Wilson-Fisher transition on fuzzy sphere bilayers
Physical Review B ( IF 3.2 ) Pub Date : 2024-09-09 , DOI: 10.1103/physrevb.110.115113
Chao Han _{1,

2} , Liangdong Hu _{1,

2} , W. Zhu _{1,

2}

Affiliation

The Wilson-Fisher criticality provides a paradigm for a large class of phase transitions in nature (e.g., helium, ferromagnets). In three dimensions, Wilson-Fisher critical points are not exactly solvable due to the strongly correlated feature, so one has to resort to nonperturbative tools such as numerical simulations. Here, we design a microscopic model of Heisenberg magnet bilayer and study the underlying Wilson-Fisher

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transition through the lens of fuzzy sphere regularization. We uncover a wealth of crucial information which directly reveals the emergent conformal symmetry regarding this fixed point. Specifically, we accurately calculate and analyze the energy spectra at the transition, and explicitly identify the existence of a conserved Noether current, a stress tensor, and relevant primary fields. Most importantly, the primaries and their descendants form a fingerprint conformal tower structure, pointing to an almost perfect state-operator correspondence. Furthermore, by examining the leading rank-4 symmetric tensor operator, we demonstrate the cubic perturbation is relevant, implying the critical

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model is unstable to cubic anisotropy, in agreement with the renormalization group and bootstrap calculations. The successful dissection of conformal content of the Wilson-Fisher universality class extends the horizon of the fuzzy sphere method and paves the way for exploring higher-dimensional conformal field theories.

中文翻译：

模糊球双层上威尔逊-费舍尔过渡的共形算子内容

威尔逊-费舍尔临界性为自然界中一大类相变（例如氦、铁磁体）提供了范例。在三维空间中，由于强相关特征，Wilson-Fisher 临界点无法精确求解，因此必须求助于数值模拟等非微扰工具。在这里，我们设计了海森堡磁双层的微观模型并研究了底层的威尔逊-费歇尔

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通过模糊球正则化的镜头进行过渡。我们发现了大量的关键信息，这些信息直接揭示了关于该不动点的新兴共形对称性。具体来说，我们准确地计算和分析了跃迁处的能谱，并明确地识别了守恒诺特电流、应力张量和相关初级场的存在。最重要的是，初选及其后代形成了指纹共形塔结构，指向近乎完美的状态运营商对应关系。此外，通过检查领先的 4 阶对称张量算子，我们证明了三次扰动是相关的，这意味着临界