Gapless symmetry-protected topological states in measurement-only circuits

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…

• NS
  National Science Foundation

  Award: MERSEC DMR 2011750
• GA
  Gordon and Betty Moore Foundation

  Awards: GBMF8685, GBMF11070
• PU
  Princeton University

  Award: 404513
• TU
  Tulane University
• NN
  National Natural Science Foundation of China

  Award: 12405034
• MO
  Ministry of Science and Technology of the People's Republic of China

  Award: 2022YFA1402701
• CP
  China Postdoctoral Science Foundation

  Award: 2024M752760