Entanglement Holography in Quantum Phases via Twisted Rényi-N Correlators
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908424950775808 |
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| author | Sala, Pablo Pollmann, Frank Oshikawa, Masaki You, Yizhi |
| author_facet | Sala, Pablo Pollmann, Frank Oshikawa, Masaki You, Yizhi |
| contents | We introduce a holographic framework for the entanglement Hamiltonian in symmetry-protected topological (SPT) phases with area-law entanglement, whose reduced density matrix $ρ\propto e^{-H_e}$ can be treated as a lower-dimensional mixed state. By replicating $ρ$, we reconstruct the fixed-point SPT wavefunction, establishing an exact correspondence between the bulk strange correlator of the (d+1)-dimensional SPT state and the twisted Rényi-N operator of the d-dimensional reduced density matrix. Notably, the reduced density matrix exhibits long-range or quasi-long-range order along the replica direction, revealing a universal entanglement feature in SPT phases. As a colloary, we generalized the framework of twisted Rényi-N correlator to thermal states and open quantum systems, providing an alternative formulation of the Lieb-Schultz-Mattis theorem, applicable to both closed and open systems. Finally, we extend our protocol to mixed-state SPT phases and introduce new quantum information metrics -- twisted Rényi-N correlators of the surgery operator -- to characterize the topology of mixed states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement Holography in Quantum Phases via Twisted Rényi-N Correlators Sala, Pablo Pollmann, Frank Oshikawa, Masaki You, Yizhi Strongly Correlated Electrons Quantum Physics We introduce a holographic framework for the entanglement Hamiltonian in symmetry-protected topological (SPT) phases with area-law entanglement, whose reduced density matrix $ρ\propto e^{-H_e}$ can be treated as a lower-dimensional mixed state. By replicating $ρ$, we reconstruct the fixed-point SPT wavefunction, establishing an exact correspondence between the bulk strange correlator of the (d+1)-dimensional SPT state and the twisted Rényi-N operator of the d-dimensional reduced density matrix. Notably, the reduced density matrix exhibits long-range or quasi-long-range order along the replica direction, revealing a universal entanglement feature in SPT phases. As a colloary, we generalized the framework of twisted Rényi-N correlator to thermal states and open quantum systems, providing an alternative formulation of the Lieb-Schultz-Mattis theorem, applicable to both closed and open systems. Finally, we extend our protocol to mixed-state SPT phases and introduce new quantum information metrics -- twisted Rényi-N correlators of the surgery operator -- to characterize the topology of mixed states. |
| title | Entanglement Holography in Quantum Phases via Twisted Rényi-N Correlators |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2506.10076 |