3D Ising CFT and Exact Diagonalization on Icosahedron: The Power of Conformal Perturbation Theory

Abstract

We consider the transverse field Ising model in $(2+1)$D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a meaningful comparison to the 3D Ising CFT on $\mathbb{R}\times S^2$, by including effective perturbations of the CFT Hamiltonian with a handful of local operators. This extreme example shows the power of conformal perturbation theory in understanding finite $N$ effects in models on regularized $S^2$. Its ideal arena of application should be the recently proposed models of fuzzy sphere regularization.

22 pages, 9 figures; v2 - footnote 5 added; v3 - typos corrected and footnotes added, subtitle added; v4 - a paragraph in conclusions added, version to appear in SciPost

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Cited by in corpus (15)

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• Studying the 3d Ising surface CFTs on the fuzzy sphere
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• Improving the five-point bootstrap
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
• A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere
• Quantum Monte Carlo Simulation of the 3D Ising Transition on the Fuzzy Sphere
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Conformal Data for the O(3) Wilson-Fisher Conformal Field Theory from Fuzzy Sphere Realization of the Quantum Rotor Model
• Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model
• A Fuzzy Sphere Journey in Critical Phenomena