We locate the phase-transition line for the Ising model on the fuzzy sphere from a finite-size scaling analysis of its ground-state energy. Our strategy is to write the latter as $E_{GS}(N_m)/N_m = E_{0} + E_1 /N_m + E_{3/2}/N_m^{3/2}+ ...$, and to search for a minimum of $ χ:=E_{3/2}/E_0$ as a function of the couplings. Conformal perturbation theory predicts that around a CFT, $χ= χ_{\rm min} + \sum_i λ_i^2 N_m^{-ω_i} + O(λ^3)$, where $λ_i$ are the couplings associated to perturbations of operators with dimension $Δ_i$, and $ω_i = d-Δ_i$. This procedure finds the critical curve of [PRX 13 (2023) 021009] and their sweet spot with good precision. Varying two coupling constants allows us to extract the correction-to-scaling exponent $ω$ associated to the two leading scalars $ε$, and $ε'$. We find similar results when normalizing by the gap to the stress tensor $T$ or first parity-odd operator $σ$ instead of $E_0$.
Graduate Group in Applied Science & Technology, University of California, Berkeley（加州大学伯克利分校应用科学与技术研究生组）；Department of Physics, Harvard University（哈佛大学物理系）；Materials Research Laboratory, Massachusetts Institute of Technology（麻省理工学院材料研究实验室）
Conformal Data for the $O(2)$ Wilson-Fisher CFT in $(2+1)$-Dimensional Spacetime from Exact Diagonalization and Matrix Product States on the Fuzzy Sphere
Laboratory for Theoretical and Computational Physics, PSI Center for Scientific Computing, Theory and Data（理论计算物理实验室）；Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Univ. Grenoble Alpes, CNRS, LPMMC（格勒诺布尔阿尔卑斯大学）；Institut des Hautes Études Scientifiques（高等科学研究所）
Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Univ. Grenoble Alpes, CNRS, LPMMC（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，凝聚态物质和磁场实验室）；Universität Innsbruck（因斯布鲁克大学）；Institut des Hautes Études Scientifiques（高等科学研究所）
The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere
C. N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学杨振宁理论物理研究所）；Perimeter Institute for Theoretical Physics（_perimeter理论物理研究所）；Department of Physics and Astronomy, University of Waterloo（滑铁卢大学物理与天文学系）
Emergence of 3D Superconformal Ising Criticality on the Fuzzy Sphere
Westlake Institute of Advanced Study, Westlake University（西湖高等研究院，西湖大学）；Institute for Advanced Study, Kyushu University（九州大学高级研究院）；School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学院）
3d Conformal Field Theories via Fuzzy Sphere Algebra
Walter Burke Institute for Theoretical Physics and Department of Physics, California Institute of Technology（加州理工学院沃尔特·伯克理论物理研究所和物理系）；Department of Mathematics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校数学系）
Conformal Data for the O(3) Wilson-Fisher Conformal Field Theory from Fuzzy Sphere Realization of the Quantum Rotor Model
Laboratory for Theoretical and Computational Physics, PSI Center for Scientific Computing, Theory and Data（理论计算物理实验室）；Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Univ. Grenoble Alpes, CNRS, LPMMC（格勒诺布尔阿尔卑斯大学）
