Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914162257428480 |
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| author | Shah, Jeet Fechisin, Christopher Wang, Yu-Xin Iosue, Joseph T. Watson, James D. Wang, Yan-Qi Ware, Brayden Gorshkov, Alexey V. Lin, Cheng-Ju |
| author_facet | Shah, Jeet Fechisin, Christopher Wang, Yu-Xin Iosue, Joseph T. Watson, James D. Wang, Yan-Qi Ware, Brayden Gorshkov, Alexey V. Lin, Cheng-Ju |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking Shah, Jeet Fechisin, Christopher Wang, Yu-Xin Iosue, Joseph T. Watson, James D. Wang, Yan-Qi Ware, Brayden Gorshkov, Alexey V. Lin, Cheng-Ju Quantum Physics Statistical Mechanics Strongly Correlated Electrons 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. |
| title | Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2410.12900 |