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 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 = S3, 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=S3, 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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BibTeX
@misc{florescalderon2026nonabelian,
title = {{Non-Abelian Anyon Condensation: a Path-Integral Monte Carlo Approach}},
author = {Rafael Flores-Calderón and Frank Pollmann and Michael Knap},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19282},
eprint = {2609.19282},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19282},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-Abelian Anyon Condensation: a Path-Integral Monte Carlo Approach
AU - Rafael Flores-Calderón
AU - Frank Pollmann
AU - Michael Knap
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19282
UR - https://arxiv.org/abs/2609.19282
AB - 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.
ER -