Gapless Symmetry-Protected Topological States in Measurement-Only Circuits

• URL: http://arxiv.org/abs/2501.03851v1
• Date: Tue, 07 Jan 2025 15:07:59 GMT
• Title: Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Authors: Xue-Jia Yu, Sheng Yang, Shuo Liu, Hai-Qing Lin, Shao-Kai Jian,
• Abstract summary: We generalize the notion of gapless symmetry-protected topological (gSPT) states to the critical steady state. We demonstrate the realization of a steady-state gSPT phase in a $mathbb Z_4$ circuit model. We provide a unified theoretical framework by mapping the system to the Majorana loop model.
• Score: 6.481398793151959
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• Abstract: 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.

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