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PreprintCC BY 4.0arXiv

From Entanglement Bootstrap to DHR Theory

  • Kohtaro Kato
  • Yoshiko Ogata
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Abstract

We establish a direct connection between the entanglement bootstrap and the Doplicher--Haag--Roberts theory of superselection sectors for two-dimensional quantum spin systems. Under the entanglement-bootstrap assumptions, we prove Haag duality and establish a one-to-one correspondence between simple entanglement-bootstrap anyon types and irreducible superselection sectors. For each fusion channel, we further construct an affine bijection from density matrices on the entanglement-bootstrap fusion space to normalized positive intertwiners in the corresponding operator-algebraic fusion channel. These results connect the entropic and operator-algebraic descriptions of anyons directly, without passing through exactly solvable lattice models.

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Cite

BibTeXRIS
BibTeX
@misc{kato2026from,
  title = {{From Entanglement Bootstrap to DHR Theory}},
  author = {Kohtaro Kato and Yoshiko Ogata},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38821},
  eprint = {2610.38821},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38821},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - From Entanglement Bootstrap to DHR Theory
AU  - Kohtaro Kato
AU  - Yoshiko Ogata
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38821
UR  - https://arxiv.org/abs/2610.38821
AB  - We establish a direct connection between the entanglement bootstrap and the Doplicher--Haag--Roberts theory of superselection sectors for two-dimensional quantum spin systems. Under the entanglement-bootstrap assumptions, we prove Haag duality and establish a one-to-one correspondence between simple entanglement-bootstrap anyon types and irreducible superselection sectors. For each fusion channel, we further construct an affine bijection from density matrices on the entanglement-bootstrap fusion space to normalized positive intertwiners in the corresponding operator-algebraic fusion channel. These results connect the entropic and operator-algebraic descriptions of anyons directly, without passing through exactly solvable lattice models.
ER  -