An entropic characterization of Haag duality
Abstract
Motivated by Haag duality in quantum spin systems, we show that Haag duality for a pair of commuting factors generated by increasing sequences of finite-dimensional matrix algebras is equivalent to the asymptotic vanishing of a suitable conditional mutual information. For spin systems, let an annulus separate a finite region from the exterior. Haag duality then holds for a region A if and only if the mutual information of the inner region and the exterior, conditioned on the part of A inside the annulus, vanishes as the outer radius becomes large. As a corollary, assuming a strict area law with subleading corrections, Haag duality holds for single cones, and it holds for unions of two or more disjoint cones precisely when the topological entanglement entropy vanishes. For translation-invariant pure states on spin chains, half-chain Haag duality is equivalent to vanishing entropy density.
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BibTeX
@misc{liu2026entropic,
title = {{An entropic characterization of Haag duality}},
author = {Ruizhi Liu and Lauritz van Luijk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.13550},
eprint = {2609.13550},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13550},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An entropic characterization of Haag duality
AU - Ruizhi Liu
AU - Lauritz van Luijk
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.13550
UR - https://arxiv.org/abs/2609.13550
AB - Motivated by Haag duality in quantum spin systems, we show that Haag duality for a pair of commuting factors generated by increasing sequences of finite-dimensional matrix algebras is equivalent to the asymptotic vanishing of a suitable conditional mutual information. For spin systems, let an annulus separate a finite region from the exterior. Haag duality then holds for a region A if and only if the mutual information of the inner region and the exterior, conditioned on the part of A inside the annulus, vanishes as the outer radius becomes large. As a corollary, assuming a strict area law with subleading corrections, Haag duality holds for single cones, and it holds for unions of two or more disjoint cones precisely when the topological entanglement entropy vanishes. For translation-invariant pure states on spin chains, half-chain Haag duality is equivalent to vanishing entropy density.
ER -