Higher-form entanglement asymmetry and topological order
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913037717340160 |
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| author | Lamas, Amanda Gatto Gliozzi, Jacopo Hughes, Taylor L. |
| author_facet | Lamas, Amanda Gatto Gliozzi, Jacopo Hughes, Taylor L. |
| contents | We extend a recently defined measure of symmetry breaking, the entanglement asymmetry, to higher-form symmetries. In particular, we focus on Abelian topological order in two dimensions, which spontaneously breaks a 1-form symmetry. Using the toric code as a primary example, we compute the entanglement asymmetry and compare it to the topological entanglement entropy. We find that while the two quantities are not strictly equivalent, both are sub-leading corrections to the area law and can serve as order parameters for the topological phase. We generalize our results to non-chiral Abelian topological order and express the maximal entanglement asymmetry in terms of the quantum dimension. Finally, we discuss how the scaling of entanglement asymmetry correctly detects topological order in the deformed toric code, where 1-form symmetry breaking persists even in a trivial phase. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-form entanglement asymmetry and topological order Lamas, Amanda Gatto Gliozzi, Jacopo Hughes, Taylor L. Strongly Correlated Electrons Quantum Physics We extend a recently defined measure of symmetry breaking, the entanglement asymmetry, to higher-form symmetries. In particular, we focus on Abelian topological order in two dimensions, which spontaneously breaks a 1-form symmetry. Using the toric code as a primary example, we compute the entanglement asymmetry and compare it to the topological entanglement entropy. We find that while the two quantities are not strictly equivalent, both are sub-leading corrections to the area law and can serve as order parameters for the topological phase. We generalize our results to non-chiral Abelian topological order and express the maximal entanglement asymmetry in terms of the quantum dimension. Finally, we discuss how the scaling of entanglement asymmetry correctly detects topological order in the deformed toric code, where 1-form symmetry breaking persists even in a trivial phase. |
| title | Higher-form entanglement asymmetry and topological order |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2510.03967 |