Truncated Rotors and the Emergence of O(3) Conformal Field Theory

by Arjun Dey (PSI)

Wednesday 28 May 2025, 15:00 → 16:00 Europe/Zurich

WHGA/021

The Wilson-Fisher fixed points of O(N) models describe universal phenomena in a broad variety of systems, ranging from magnets and superfluid transitions to classical fluids and relativistic scalar field theories. We introduce a general method to investigate O(N) criticality with truncated quantum rotor models, specializing to the O(3) model on a fuzzy sphere. Applying conformal perturbation theory, we locate the critical point, compute scaling dimensions via the state-operator correspondence, and extract operator product expansion (OPE) coefficients from finite-size effects, effectively turning noise into signal. Our investigation uncovers a variety of new operators, including an O(3) pseudoscalar Lorentz vector that solves a long-standing puzzle in critical exponents of dimerized antiferromagnets. Furthermore, the appearance of the stress-energy tensor and the conserved Noether current in the spectrum attest to the presence of conformal symmetry.