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

• URL: http://arxiv.org/abs/2410.08205v2
• Date: Fri, 14 Feb 2025 00:31:28 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 S and global symmetry G corresponds to a d-dimensional mSPT with strong S and weak G symmetries. We discuss several implications of this holographic duality, including a method for preparing intrinsic mSPT states through the duality.
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• 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 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 R\'enyi-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.

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