Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems

• URL: http://arxiv.org/abs/2410.08205v1
• Date: Thu, 10 Oct 2024 17:59:42 GMT
• Title: Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Authors: Shijun Sun, Jian-Hao Zhang, Zhen Bi, Yizhi You,
• Abstract summary: 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 $mathcalS$ corresponds to a d-dimensional mSPT with strong $mathcalS$ and weak $mathcalG$ symmetries.
• Score: 4.416740212467273
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\mathcal{S}$ and global symmetry $\mathcal{G}$ corresponds to a d-dimensional mSPT with strong $\mathcal{S}$ and weak $\mathcal{G}$ 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 Renyi-N correlators can diagnose these nontrivial phases and explore their connection to strange correlators in pure-state SSPTs.

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