Flowing from the Ising Model on the Fuzzy Sphere to the 3D Lee-Yang CFT

TL;DR

This paper uses the Fuzzy Sphere regulator to study the 3D Lee-Yang conformal field theory by analyzing a deformed Ising model, identifying the critical point, and comparing spectral data with theoretical predictions.

Contribution

It introduces a method to connect the Ising model on the Fuzzy Sphere with the 3D Lee-Yang CFT and provides numerical estimates for critical properties and operator dimensions.

Findings

Critical point matches the 3D Lee-Yang CFT

Lowest-lying states align with CFT spectrum

Fuzzy Sphere estimates agree with five-loop epsilon-expansion

Abstract

We employ the Fuzzy Sphere regulator to study the 3D Lee-Yang CFT. The model is defined by deforming the Ising model on the Fuzzy Sphere via a purely imaginary longitudinal magnetic field. This model undergoes a quantum phase transition, whose critical point we determine and identify with the 3D Lee-Yang CFT. We show how to tune the model and find that the lowest-lying states of the Hamiltonian align well with the expected CFT spectrum. We discuss the Fuzzy Sphere estimates for the scaling dimension $\Delta_\phi$ of the lowest primary operator. Finally, we interpret small deviations from the CFT expectations in terms of the leading irrelevant operators of the Lee-Yang CFT. We show that the Fuzzy Sphere calculations are compatible with the best five-loop $\epsilon$-expansion estimates.