Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement

Fuente: arXiv
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Main Authors: Hsin, Po-Shen, Kobayashi, Ryohei, Prem, Abhinav
Format: Preprint
Published: 2025
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author Hsin, Po-Shen
Kobayashi, Ryohei
Prem, Abhinav
author_facet Hsin, Po-Shen
Kobayashi, Ryohei
Prem, Abhinav
contents We show that generic gapped quantum many-body states which respect an anomalous finite higher-form symmetry have an exponentially small overlap with any short-range entangled (SRE) state. Hence, anomalies of higher-form symmetries enforce $intrinsic$ long-range entanglement, which is in contrast with anomalies of ordinary (0-form) symmetries which are compatible with symmetric SRE states (specifically, symmetric cat states). As an application, we show that the anomalies of strong higher-form symmetries provide a diagnostic for mixed-state topological order in $d \geq 2$ spatial dimensions. We also identify a new (3+1)D intrinsic mixed-state topological order that does not obey remote-detectability by local decoherence of the (3+1)D Toric Code with fermionic loop excitations. This breakdown of remote detectability, as encoded in anomalies of strong higher-form symmetries, provides a partial characterization of intrinsically mixed-state topological order.
format Preprint
id arxiv_https___arxiv_org_abs_2504_10569
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement
Hsin, Po-Shen
Kobayashi, Ryohei
Prem, Abhinav
Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
We show that generic gapped quantum many-body states which respect an anomalous finite higher-form symmetry have an exponentially small overlap with any short-range entangled (SRE) state. Hence, anomalies of higher-form symmetries enforce $intrinsic$ long-range entanglement, which is in contrast with anomalies of ordinary (0-form) symmetries which are compatible with symmetric SRE states (specifically, symmetric cat states). As an application, we show that the anomalies of strong higher-form symmetries provide a diagnostic for mixed-state topological order in $d \geq 2$ spatial dimensions. We also identify a new (3+1)D intrinsic mixed-state topological order that does not obey remote-detectability by local decoherence of the (3+1)D Toric Code with fermionic loop excitations. This breakdown of remote detectability, as encoded in anomalies of strong higher-form symmetries, provides a partial characterization of intrinsically mixed-state topological order.
title Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement
topic Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
url https://arxiv.org/abs/2504.10569