Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908937609019392 |
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| author | Yu, Xue-Jia Yang, Sheng Liu, Shuo Lin, Hai-Qing Jian, Shao-Kai |
| author_facet | Yu, Xue-Jia Yang, Sheng Liu, Shuo Lin, Hai-Qing Jian, Shao-Kai |
| contents | Measurement-only quantum circuits offer a versatile platform for realizing intriguing quantum phases of matter. However, gapless symmetry-protected topological (gSPT) states remain insufficiently explored in these settings. In this Letter, we generalize the notion of gSPT to the critical steady state by investigating measurement-only circuits. Using large-scale Clifford circuit simulations, we investigate the steady-state phase diagram across several families of measurement-only circuits that exhibit topological nontrivial edge states at criticality. In the Ising cluster circuits, we uncover a symmetry-enriched non-unitary critical point, termed symmetry-enriched percolation, characterized by both topologically nontrivial edge states and string operator. Additionally, we demonstrate the realization of a steady-state gSPT phase in a $\mathbb Z_4$ circuit model. This phase features topological edge modes and persists within steady-state critical phases under symmetry-preserving perturbations. Furthermore, we provide a unified theoretical framework by mapping the system to the Majorana loop model, offering deeper insights into the underlying mechanisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03851 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gapless Symmetry-Protected Topological States in Measurement-Only Circuits Yu, Xue-Jia Yang, Sheng Liu, Shuo Lin, Hai-Qing Jian, Shao-Kai Strongly Correlated Electrons Statistical Mechanics Quantum Physics Measurement-only quantum circuits offer a versatile platform for realizing intriguing quantum phases of matter. However, gapless symmetry-protected topological (gSPT) states remain insufficiently explored in these settings. In this Letter, we generalize the notion of gSPT to the critical steady state by investigating measurement-only circuits. Using large-scale Clifford circuit simulations, we investigate the steady-state phase diagram across several families of measurement-only circuits that exhibit topological nontrivial edge states at criticality. In the Ising cluster circuits, we uncover a symmetry-enriched non-unitary critical point, termed symmetry-enriched percolation, characterized by both topologically nontrivial edge states and string operator. Additionally, we demonstrate the realization of a steady-state gSPT phase in a $\mathbb Z_4$ circuit model. This phase features topological edge modes and persists within steady-state critical phases under symmetry-preserving perturbations. Furthermore, we provide a unified theoretical framework by mapping the system to the Majorana loop model, offering deeper insights into the underlying mechanisms. |
| title | Gapless Symmetry-Protected Topological States in Measurement-Only Circuits |
| topic | Strongly Correlated Electrons Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2501.03851 |