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Modular commutator as a robust topological invariant and approximate Markovianity — arXiv:2609.09019

Source

arXiv (en)

Original

https://arxiv.org/abs/2609.09019

License (as archived)

CC0-1.0

Archived

2026-10-16T15:44:49.595Z

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793d05dd4aa899bfb3b2eaa8a25adcccb4b12dec0c58eb4c8460bfd6d8794c0a

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Modular commutator as a robust topological invariant and approximate Markovianity — arXiv:2609.09019 — arXiv (en), https://arxiv.org/abs/2609.09019 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_880cf75e91ef (Metraipolis archive dc_880cf75e91ef, sha256 793d05dd4aa899bfb3b2eaa8a25adcccb4b12dec0c58eb4c8460bfd6d8794c0a)

@misc{dc880cf75e91ef,
  title = {Modular commutator as a robust topological invariant and approximate Markovianity — arXiv:2609.09019},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.09019},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_880cf75e91ef; sha256 793d05dd4aa899bfb3b2eaa8a25adcccb4b12dec0c58eb4c8460bfd6d8794c0a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.09019. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The modular commutator provides a bulk, local, single-wave-function probe of the chiral central charge $c_-$ for gapped ground states. Its invariance under deformations was previously established under a local quantum Markov condition---namely, the conditional mutual information $I(A:C|B)$ is zero for all tripartitions of a disk into three consecutive strips A, B, and C \cite{Modular-commutator-Gapped}. However, the local quantum Markov condition also forces the probe to vanish, leaving open whether modular commutator remains robust in physically relevant states where the Markov property holds only approximately. In this paper, we resolve this tension for finite-dimensional Hilbert spaces: the approximate local quantum Markov property implies the change of the modular commutator under topology-preserving deformations vanishes asymptotically. We next prove trace-norm continuity of the modular commutator. Combining deformation invariance with trace-norm continuity, we establish that the modular commutator remains asymptotically invariant within gapped quantum phases connected by quasi-local unitary paths that preserve the approximate local quantum Markov condition. Conversely, by analyzing finite-time dynamics generated by modular Hamiltonians, we derive a quantitative lower bound on the conditional mutual information required for a non-zero modular commutator: $I(A:C|B)$ across such strip tripartitions cannot decay faster than exponentially with the width of B given that the state satisfies entanglement area law, extending the exact no-go theorem of \cite{strict-J-2024} to a quantitative finite bound . Finally, we demonstrate that those conclusions apply equally to the Hall conductance estimator \cite{FanSahayVishwanath2023}.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-09 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph) ; Strongly Correlated Electrons (cond-mat.str-el).
Pagina del lavoro: https://arxiv.org/abs/2609.09019 — 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 2026-10-16T15:32:34.881Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).