Non-Abelian Anyon Condensation: a Path-Integral Monte Carlo Approach

Abstract: Transitions out of non-Abelian topological order are difficult to describe in microscopic quantum models with numerical methods that remain tractable at large scales. We develop a sign-free path-integral framework for Kitaev quantum doubles $\mathcal D(G)$ by organizing single-link perturbations in terms of non-invertible electric and magnetic 1-form symmetries that proliferate distinct anyon species. For any finite group $G$, an exact $\textit{matterization}$ isometry introduces vertex degrees of freedom and maps the link-only model onto a $G$ gauge--Higgs theory. Furthermore, the 1-form symmetries of the fixed point allow us to define generalized Fredenhagen--Marcu order parameters that become finite when the corresponding anyons condense. For $G = S_3$, quantum Monte Carlo simulations show that proliferating a non-Abelian electric anyon drives a first-order transition in which all nontrivial electric anyons condense. In the purely magnetic limit, the model reduces to a $(2+1)$D pure $G$ gauge theory; for $G=S_3$, it exhibits a first-order confinement transition, diagnosed by the onset of a Wilson-loop area law and the restoration of an emergent magnetic 1-form symmetry. These results provide a unified numerical framework for non-Abelian anyon condensation, confinement, and generalized symmetry breaking.