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Remarks on invertible phases with non-onsite symmetry — arXiv:2609.12042

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.12042
License (as archived): CC0-1.0
Archived: 2026-10-16T04:03:46.580Z
SHA-256 of the archived text: e32cf47a8e2e52225c7841e5df45c54a62a5b81b1e18ce8f34040682b739d864
Stable URL of this page: https://metraipolis.com/documento/dc_fa200436004b

How to cite

Remarks on invertible phases with non-onsite symmetry — arXiv:2609.12042 — arXiv (en), https://arxiv.org/abs/2609.12042 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fa200436004b (Metraipolis archive dc_fa200436004b, sha256 e32cf47a8e2e52225c7841e5df45c54a62a5b81b1e18ce8f34040682b739d864)

BibTeX

@misc{dcfa200436004b,
  title = {Remarks on invertible phases with non-onsite symmetry — arXiv:2609.12042},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.12042},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fa200436004b; sha256 e32cf47a8e2e52225c7841e5df45c54a62a5b81b1e18ce8f34040682b739d864},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.12042. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study invertible phases protected by non-onsite symmetries carrying nontrivial lattice anomaly indices. While lattice anomalies are usually viewed as obstructions to symmetric short-range-entangled (SRE) states, we show that anomalous lattice symmetries can nevertheless admit invertible phases that are not SRE, and can moreover shift the set of symmetry-compatible invertible phases. In particular, we consider a fermionic $\mathbb Z_4^F$ symmetry in (2+1) dimensions. For an onsite $\mathbb Z_4^F$ symmetry, symmetric invertible phases have integer chiral central charge $c_-\in\mathbb Z$, whereas a non-onsite symmetry with nontrivial lattice anomaly index obstructs all such phases despite having trivial continuum 't Hooft anomaly. We resolve this by constructing an exact exponentially quasi-local $\mathbb Z_4^F$ symmetry of a $p+ip$ superconductor with $c_-=1/2$. We compute its lattice anomaly, and find that the symmetry indeed forbids $c_-\in \mathbb{Z}$ invertible states. The allowed invertible phases are consequently shifted to $c_-\in\mathbb Z+1/2$. By gauging the fermion parity of the $p+ip$ superconductor, one obtains an Ising topological order enriched by a $\mathbb Z_4$ symmetry. We describe the corresponding symmetry structure in terms of a fusion 2-category. We further show that the $p+ip$ state admits an enlarged non-onsite $U(1)^f$ symmetry, providing an analogue of fractional quantum Hall response in an invertible phase. This non-onsite $U(1)^f$ symmetry again forbids Chern insulators carrying $c_-\in\mathbb{Z}$, while being compatible with invertible states with $c_-\in\mathbb{Z}+1/2$. This result motivates a systematic study of new classes of invertible phases and spin liquids enriched by non-onsite symmetries.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-14 in quant-ph).
Categorie arXiv: Strongly Correlated Electrons (cond-mat.str-el) ; High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.12042 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T03:55:40.589Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).