Non-abelian symmetry-resolved entanglement entropy
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916468114849792 |
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| author | Bianchi, Eugenio Dona, Pietro Kumar, Rishabh |
| author_facet | Bianchi, Eugenio Dona, Pietro Kumar, Rishabh |
| contents | We introduce a mathematical framework for symmetry-resolved entanglement entropy with a non-abelian symmetry group. To obtain a reduced density matrix that is block-diagonal in the non-abelian charges, we define subsystems operationally in terms of subalgebras of invariant observables. We derive exact formulas for the average and the variance of the typical entanglement entropy for the ensemble of random pure states with fixed non-abelian charges. We focus on compact, semisimple Lie groups. We show that, compared to the abelian case, new phenomena arise from the interplay of locality and non-abelian symmetry, such as the asymmetry of the entanglement entropy under subsystem exchange, which we show in detail by computing the Page curve of a many-body system with SU(2) symmetry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_00597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-abelian symmetry-resolved entanglement entropy Bianchi, Eugenio Dona, Pietro Kumar, Rishabh Quantum Physics Statistical Mechanics Strongly Correlated Electrons General Relativity and Quantum Cosmology High Energy Physics - Theory We introduce a mathematical framework for symmetry-resolved entanglement entropy with a non-abelian symmetry group. To obtain a reduced density matrix that is block-diagonal in the non-abelian charges, we define subsystems operationally in terms of subalgebras of invariant observables. We derive exact formulas for the average and the variance of the typical entanglement entropy for the ensemble of random pure states with fixed non-abelian charges. We focus on compact, semisimple Lie groups. We show that, compared to the abelian case, new phenomena arise from the interplay of locality and non-abelian symmetry, such as the asymmetry of the entanglement entropy under subsystem exchange, which we show in detail by computing the Page curve of a many-body system with SU(2) symmetry. |
| title | Non-abelian symmetry-resolved entanglement entropy |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.00597 |