Quantum Monte Carlo simulation of the 3D Ising transition on the fuzzy sphere

We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere Phys. Rev. X 13, 021009 (2023). By introducing an additional SU(2) layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.