Topological quantum critical points exhibit anomalous dynamical scaling in boundary dynamics and defect production due to edge modes, beyond conventional Kibble-Zurek scaling.
Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
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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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PT symmetry enriches non-Hermitian critical points with topological nontriviality, robust edge modes, and a quantized imaginary subleading term in entanglement entropy scaling.
Long-range competing two- and three-qubit measurements in quantum circuits produce measurement-range-dependent steady states featuring SPT order and non-area-law entanglement.
Derives exact bulk-boundary correspondence allowing extraction of edge-mode degeneracy from bulk entanglement spectrum in critical free-fermion systems of arbitrary dimensions.
Deconfined criticality in a 1D lattice model is shown to be an intrinsically gapless topological state whose mixed anomaly enforces robust edge modes without gapped counterparts.
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PT symmetry-enriched non-unitary criticality
PT symmetry enriches non-Hermitian critical points with topological nontriviality, robust edge modes, and a quantized imaginary subleading term in entanglement entropy scaling.