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

TL;DR

This paper establishes a holographic duality linking mixed-state symmetry-protected topological phases in open quantum systems to higher-dimensional subsystem SPTs, enabling new analysis tools for mixed states and insights into intrinsic topological phases.

Contribution

It introduces a novel holographic duality between mixed-state SPTs and higher-dimensional SSPTs, providing a new framework for studying open quantum system topological phases.

Findings

Mapping between reduced density matrices and SSPT wavefunctions

Diagnosis of nontrivial phases via strange correlators

Potential method for preparing intrinsic mSPT states

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.