The Operator Product Expansion for Radial Lattice Quantization of 3D ${\varphi }^4$ Theory

Abstract

At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3d Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the Quantum Finite Elements method to implement radially quantized critical ${\varphi }^4$ theory on simplicial lattices approaching $\mathbb{R}\times S^2$. Computing the four-point function of identical scalars, we demonstrate the power of radial quantization by the accurate determination of the scaling dimensions ${\Delta }_{\epsilon }$ and ${\Delta }_T$ as well as ratios of the operator product expansion (OPE) coefficients $f_{\sigma \sigma \epsilon }$ and $f_{\sigma \sigma T}$ of the first spin-0 and spin-2 primary operators $\epsilon$ and $T$ of the 3d Ising CFT.

16 pages, 10 figures

References in corpus (5)

• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• Two- and three-point functions at criticality: Monte Carlo simulations of the improved three-dimensional Blume-Capel model
• Conformal four-point correlators of the 3D Ising transition via the quantum fuzzy sphere
• Numerical estimation of structure constants in the 3d Ising CFT through Markov chain UV sampler

Cited by in corpus (1)

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