标题： 精确对角化、矩阵乘积态和共形微扰理论研究三维伊辛模糊球模型 显示英文标题

标题： Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model

摘要： 统计和量子格点模型中相变的数值研究为相应的共形场论（CFTs）提供了至关重要的见解。 在更高维度中，通过选择球面 $S^{d-1}$ 作为空间流形，可以方便地将有限体积的数值结果与无限体积的CFT数据进行比较。 最近，模糊球正则化方法在参考文献 [Zhu等, Phys. Rev. X 13 021009 (2023)] 中的应用使得这类研究能够实现精确的旋转不变性，取得了与已知三维Ising CFT预测令人印象深刻的吻合，同时也得到了新的结果。 然而，系统性的改进以及对有限大小校正的更深入理解仍然是必不可少的。 在这项工作中，我们重新审视了模糊球正则化方法，专注于原始的Ising模型，有两个主要目标。 首先，我们使用共形微扰理论（CPT）评估这种方法的稳健性，并提供详细的指导手册。 我们展示了如何利用CPT为确定临界点、光速以及偏离CFT预测的残余偏差提供统一框架。 应用这一框架，我们研究了有限大小校正，并阐明了调整模型以最小化这些效应的作用。 其次，我们开发了一种从模糊球数据中提取算符乘积展开（OPE）系数的新方法。 该方法利用能量水平对偏离临界性的敏感性，为有限系统的能级混合和避免交叉提供了新的见解。 我们的工作还包括验证了在远离可积极限的1+1维Ising模型中的CPT。 显示英文摘要

摘要： Numerical studies of phase transitions in statistical and quantum lattice models provide crucial insights into the corresponding Conformal Field Theories (CFTs). In higher dimensions, comparing finite-volume numerical results to infinite-volume CFT data is facilitated by choosing the sphere $S^{d-1}$ as the spatial manifold. Recently, the fuzzy sphere regulator in Ref. [Zhu et al, Phys. Rev. X 13 021009 (2023)] has enabled such studies with exact rotational invariance, yielding impressive agreement with known 3D Ising CFT predictions, as well as new results. However, systematic improvements and a deeper understanding of finite-size corrections remain essential. In this work, we revisit the fuzzy sphere regulator, focusing on the original Ising model, with two main goals. First, we assess the robustness of this approach using Conformal Perturbation Theory (CPT), to which we provide a detailed guidebook. We demonstrate how CPT provides a unified framework for determining the critical point, the speed of light, and residual deviations from CFT predictions. Applying this framework, we study finite-size corrections and clarify the role of tuning the model in minimizing these effects. Second, we develop a novel method for extracting Operator Product Expansion (OPE) coefficients from fuzzy sphere data. This method leverages the sensitivity of energy levels to detuning from criticality, providing new insights into level mixing and avoided crossings in finite systems. Our work also includes validation of CPT in a 1+1D Ising model away from the integrable limit.