Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking

• URL: http://arxiv.org/abs/2410.12900v1
• Date: Wed, 16 Oct 2024 18:00:00 GMT
• Title: Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
• Authors: Jeet Shah, Christopher Fechisin, Yu-Xin Wang, Joseph T. Iosue, James D. Watson, Yan-Qi Wang, Brayden Ware, Alexey V. Gorshkov, Cheng-Ju Lin,
• Abstract summary: We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. We find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. We construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.
• Score: 14.693424479293737
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• Abstract: Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-state nonequilibrium quantum phases. We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. Focusing on the decohered cluster state -- a mixed-state symmetry-protected topological state protected by a combined strong and weak symmetry -- we construct a parent Lindbladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical and numerical methods, we find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. However, when perturbations introduce only weak symmetry defects, the steady-state mixed-state symmetry-protected topological order remains stable. Additionally, we construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.

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