Non-Abelian Anyon Condensation: a Path-Integral Monte Carlo Approach
cond-mat.str-el, hep-lat, quant-ph
Submitted: 2026-09-16
Updated: 2026-09-16
License: http://creativecommons.org/licenses/by/4.0/
The gist: Transitions out of non-Abelian topological order are difficult to describe in microscopic quantum models with numerical methods that remain tractable at large scales.
Terminology
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 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 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.
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