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PreprintCC BY 4.0arXiv

Proliferation Transitions for Quantum Doubles of Groups

  • Yuhan Gai
  • Sakura Schafer-Nameki
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Abstract

Proliferation transitions are phase transitions between a 2+1d topological order 𝒯 and another 𝒯/π’œ, obtained by condensing anyons in an algebra π’œβŠ‚ 𝒯. We consider such transitions in quantum doubles of groups, 𝒯=D(G, Ο‰), for finite groups G possibly with three-cocycle Ο‰, for which condensable algebras are fully classified. Given a condensable algebra π’œ, we represent 𝒯 in terms of a Symmetry Topological Field Theory (SymTFT), that is tailored to the π’œ proliferation transition. The SymTFT bulk is constructed from the MΓΌger center of the subcategory generated by the algebra, i.e. the category of transparent lines, which can be bosons or fermions. Properties of the transition can then be inferred directly from the algebra classification data. For gauged Landau-Ginzburg (LG*) type transitions, we show that they do not only depend on the anyons in π’œ through their field content, but the cubic interactions are fixed in terms of the multiplication structure of π’œ. Applied to twin algebras, which have the same anyon content but different multiplication structures, we show that twins result in distinct proliferation transitions.

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Cite

BibTeXRIS
BibTeX
@misc{gai2026proliferation,
  title = {{Proliferation Transitions for Quantum Doubles of Groups}},
  author = {Yuhan Gai and Sakura Schafer-Nameki},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28253},
  eprint = {2610.28253},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28253},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Proliferation Transitions for Quantum Doubles of Groups
AU  - Yuhan Gai
AU  - Sakura Schafer-Nameki
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28253
UR  - https://arxiv.org/abs/2610.28253
AB  - Proliferation transitions are phase transitions between a 2+1d topological order 𝒯 and another 𝒯/π’œ, obtained by condensing anyons in an algebra π’œβŠ‚ 𝒯. We consider such transitions in quantum doubles of groups, 𝒯=D(G, Ο‰), for finite groups G possibly with three-cocycle Ο‰, for which condensable algebras are fully classified. Given a condensable algebra π’œ, we represent 𝒯 in terms of a Symmetry Topological Field Theory (SymTFT), that is tailored to the π’œ proliferation transition. The SymTFT bulk is constructed from the MΓΌger center of the subcategory generated by the algebra, i.e. the category of transparent lines, which can be bosons or fermions. Properties of the transition can then be inferred directly from the algebra classification data. For gauged Landau-Ginzburg (LG*) type transitions, we show that they do not only depend on the anyons in π’œ through their field content, but the cubic interactions are fixed in terms of the multiplication structure of π’œ. Applied to twin algebras, which have the same anyon content but different multiplication structures, we show that twins result in distinct proliferation transitions.
ER  -