Entanglement asymmetry for higher and noninvertible symmetries
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| author | Benini, Francesco Calabrese, Pasquale Fossati, Michele Singh, Amartya Harsh Venuti, Marco |
| author_facet | Benini, Francesco Calabrese, Pasquale Fossati, Michele Singh, Amartya Harsh Venuti, Marco |
| contents | Entanglement asymmetry is an observable in quantum systems, constructed using quantum-information methods, suited to detecting symmetry breaking in states -- possibly out of equilibrium -- relative to a subsystem. In this paper we define the asymmetry for generalized finite symmetries, including higher-form and noninvertible ones. To this end, we introduce a "symmetrizer" of (reduced) density matrices with respect to the $C^*$-algebra of symmetry operators acting on the subsystem Hilbert space. We study in detail applications to (1+1)-dimensional quantum field theories: First, we analyze spontaneous symmetry breaking of noninvertible symmetries, confirming that distinct vacua can exhibit different physical properties. Second, we compute the asymmetry of certain excited states in conformal field theories (including the Ising CFT), when the subsystem is either the full circle or an interval therein. The relevant symmetry algebras to consider are the fusion, tube, and strip algebras. Finally, we comment on the case that the symmetry algebra is a (weak) Hopf algebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_16311 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement asymmetry for higher and noninvertible symmetries Benini, Francesco Calabrese, Pasquale Fossati, Michele Singh, Amartya Harsh Venuti, Marco High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons Quantum Physics Entanglement asymmetry is an observable in quantum systems, constructed using quantum-information methods, suited to detecting symmetry breaking in states -- possibly out of equilibrium -- relative to a subsystem. In this paper we define the asymmetry for generalized finite symmetries, including higher-form and noninvertible ones. To this end, we introduce a "symmetrizer" of (reduced) density matrices with respect to the $C^*$-algebra of symmetry operators acting on the subsystem Hilbert space. We study in detail applications to (1+1)-dimensional quantum field theories: First, we analyze spontaneous symmetry breaking of noninvertible symmetries, confirming that distinct vacua can exhibit different physical properties. Second, we compute the asymmetry of certain excited states in conformal field theories (including the Ising CFT), when the subsystem is either the full circle or an interval therein. The relevant symmetry algebras to consider are the fusion, tube, and strip algebras. Finally, we comment on the case that the symmetry algebra is a (weak) Hopf algebra. |
| title | Entanglement asymmetry for higher and noninvertible symmetries |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2509.16311 |