Bootstrapping Heisenberg magnets and their cubic instability
Shai M. Chester, Walter Landry, Junyu Liu, David Poland, David Simmons–Duffin, Ning Su, Alessandro Vichi
Abstract
We study the critical O(3) model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of conformal field theory data from correlators involving the leading O(3) singlet s, vector φ, and rank-2 symmetric tensor t. We determine their scaling dimensions to be (Δφ,Δs,Δt)=(0.518942(51),1.59489(59),1.20954(23)), and also bound various operator product expansion coefficients. We additionally introduce a new "tip-finding"algorithm to compute an upper bound on the leading rank-4 symmetric tensor t4, which we find to be relevant with Δt4<2.99056. The conformal bootstrap thus provides a numerical proof that systems described by the critical O(3) model, such as classical Heisenberg ferromagnets at the Curie transition, are unstable to cubic anisotropy.