A nonabelian anyon violates Haag duality

@misc{wallick2026nonabelian,
  title = {{A nonabelian anyon violates Haag duality}},
  author = {Daniel Wallick and Henrik Wilming},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01267},
  eprint = {2609.01267},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01267},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - A nonabelian anyon violates Haag duality
AU  - Daniel Wallick
AU  - Henrik Wilming
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01267
UR  - https://arxiv.org/abs/2609.01267
AB  - We show that a superselction sector describing a single nonabelian anyon violates Haag duality, which is equivalent to the fundamental quantum-information theoretic principle of uniqueness of purifications. We provide a simple physics argument as well as a rigorous proof using sector theory, and instantiate our result concretely in Levin-Wen models. We also show that the associated ground state does not allow for quantum steering despite being a pure state. Finally, we show that this ground state violates approximate Haag duality, disproving the conjecture that all gapped ground states satisfy this condition. Our result implies that there are gapped phases of matter where Haag duality fails at every point in the phase.
ER  -