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Peer-reviewedCC BY 4.0SciPost Physics

Irrational CFTs from coupled anyon chains with non-invertible symmetries?

  • António Antunes
  • Junchen Rong
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Abstract

Irrational CFTs in 1+1d with a discrete spectrum and no conserved currents other than the stress-tensor are expected to be generic, unsolvable by standard methods, and hard to construct explicitly. We introduce a lattice model that realizes a candidate for such a CFT as a conformal phase of matter without fine-tuning. The model is constructed by coupling N≥2 golden anyon chains together, preserving N copies of the Fibonacci non-invertible symmetry. We use the MPS/DMRG approach to study this model numerically, which allows us to calculate the corresponding conformal data, obtaining hints of its irrationality. As a byproduct of our analysis, we provide an extensive list of rational CFTs with $1

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Cite

BibTeXRIS
BibTeX
@article{antunes2026irrational,
  title = {{Irrational CFTs from coupled anyon chains with non-invertible symmetries?}},
  author = {António Antunes and Junchen Rong},
  journal = {SciPost Physics},
  year = {2026},
  month = jul,
  doi = {10.21468/scipostphys.21.1.005},
  eprint = {2507.14280},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05193579v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Irrational CFTs from coupled anyon chains with non-invertible symmetries?
AU  - António Antunes
AU  - Junchen Rong
PY  - 2026
DA  - 2026/07/06
JO  - SciPost Physics
DO  - 10.21468/scipostphys.21.1.005
UR  - https://hal.science/hal-05193579v1
AB  - Irrational CFTs in 1+1d with a discrete spectrum and no conserved currents other than the stress-tensor are expected to be generic, unsolvable by standard methods, and hard to construct explicitly. We introduce a lattice model that realizes a candidate for such a CFT as a conformal phase of matter without fine-tuning. The model is constructed by coupling N≥2 golden anyon chains together, preserving N copies of the Fibonacci non-invertible symmetry. We use the MPS/DMRG approach to study this model numerically, which allows us to calculate the corresponding conformal data, obtaining hints of its irrationality. As a byproduct of our analysis, we provide an extensive list of rational CFTs with $1
SN  - 2542-4653
ER  -