Interacting Chern Insulator Transition on the Sphere: Revealing the Gross-Neveu-Yukawa Criticality

In two dimensions a Chern insulator can be tuned from a topological state to an ordinary band insulator without breaking any symmetry, offering a clean example of "beyond-Landau" criticality. We show that electron interactions drive this transition to the Gross-Neveu-Yukawa (GNY) fixed point, a benchmark problem of broad interest across high-energy and condensed-matter physics. By solving the minimal Dirac model on the surface of a sphere, we obtain the full spectrum of critical excitations from systems containing only a few electrons. The leading critical exponents match state-of-the-art bootstrap bounds, and several previously unseen collective modes appear. Our results demonstrate that placing a Dirac cone on a curved geometry provides a surprisingly simple and accurate setup for strongly interacting topological transitions.