Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915295306711040 |
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| author | Sun, Shijun Zhang, Jian-Hao Bi, Zhen You, Yizhi |
| author_facet | Sun, Shijun Zhang, Jian-Hao Bi, Zhen You, Yizhi |
| contents | We establish a holographic duality between d-dimensional mixed-state symmetry-protected topological phases (mSPTs) and (d+1)-dimensional subsystem symmetry-protected topological states (SSPTs). Specifically, we show that the reduced density matrix of the boundary layer of a (d+1)-dimensional SSPT with subsystem symmetry S and global symmetry G corresponds to a d-dimensional mSPT with strong S and weak G symmetries. Conversely, we demonstrate that the wavefunction of an SSPT can be constructed by replicating the density matrix of the corresponding lower-dimensional mSPT. This mapping links the density matrix in lower dimensions to the entanglement properties of higher-dimensional wavefunctions, providing an approach for analyzing nonlinear quantities and quantum information metrics in mixed-state systems. Our duality offers a new perspective for studying intrinsic mSPTs that are unique to open quantum systems, without pure state analogs. We show that strange correlators and twisted Rényi-N correlators can diagnose these nontrivial phases and explore their connection to strange correlators in pure-state SSPTs. Furthermore, we discuss several implications of this holographic duality, including a method for preparing intrinsic mSPT states through the duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08205 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems Sun, Shijun Zhang, Jian-Hao Bi, Zhen You, Yizhi Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory We establish a holographic duality between d-dimensional mixed-state symmetry-protected topological phases (mSPTs) and (d+1)-dimensional subsystem symmetry-protected topological states (SSPTs). Specifically, we show that the reduced density matrix of the boundary layer of a (d+1)-dimensional SSPT with subsystem symmetry S and global symmetry G corresponds to a d-dimensional mSPT with strong S and weak G symmetries. Conversely, we demonstrate that the wavefunction of an SSPT can be constructed by replicating the density matrix of the corresponding lower-dimensional mSPT. This mapping links the density matrix in lower dimensions to the entanglement properties of higher-dimensional wavefunctions, providing an approach for analyzing nonlinear quantities and quantum information metrics in mixed-state systems. Our duality offers a new perspective for studying intrinsic mSPTs that are unique to open quantum systems, without pure state analogs. We show that strange correlators and twisted Rényi-N correlators can diagnose these nontrivial phases and explore their connection to strange correlators in pure-state SSPTs. Furthermore, we discuss several implications of this holographic duality, including a method for preparing intrinsic mSPT states through the duality. |
| title | Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems |
| topic | Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.08205 |