Gapless Symmetry-Protected Topological States in Measurement-Only Circuits

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.

5.5 pages with supplemental materials, 16 figures

References in corpus (52)

• The density-matrix renormalization group in the age of matrix product states
• Matrix product states represent ground states faithfully
• Random Quantum Circuits
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Measurement-induced entanglement and teleportation on a noisy quantum processor
• Measurement-induced dark state phase transitions in long-ranged fermion systems
• SYK meets non-Hermiticity II: measurement-induced phase transition
• Entanglement Transition in the Projective Transverse Field Ising Model
• Fate of measurement-induced phase transition in long-range interactions
• Symmetry enriched phases of quantum circuits
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• Measurement as a shortcut to long-range entangled quantum matter
• Spacetime duality between localization transitions and measurement-induced transitions
• Measurements conspire nonlocally to restructure critical quantum states
• The Prediction of a Gapless Topological "Haldane Liquid" Phase in a One-Dimensional Cold Polar Molecular Lattice
• Transitions in the learnability of global charges from local measurements
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Mixed-state long-range order and criticality from measurement and feedback
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Emergent Replica Conformal Symmetry in Non-Hermitian SYK${}_2$ Chains
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• Probing post-measurement entanglement without post-selection
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• Majorana Loop Models for Measurement-Only Quantum Circuits
• Decorated Defect Construction of Gapless-SPT States
• Topological holography, quantum criticality, and boundary states
• Neural-Network Decoders for Measurement Induced Phase Transitions
• Universal entanglement spectrum in gapless symmetry protected topological states
• Universal KPZ scaling in noisy hybrid quantum circuits
• Decodable hybrid dynamics of open quantum systems with Z_2 symmetry
• Entanglement Structure and Information Protection in Noisy Hybrid Quantum Circuits
• Noise-induced phase transitions in hybrid quantum circuits
• Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations
• Detecting and stabilizing measurement-induced symmetry-protected topological phases in generalized cluster models
• Absence of logarithmic and algebraic scaling entanglement phases due to skin effect
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Quantum phase transition and critical behavior between the gapless topological phases
• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
• Quantum phase transition between topologically distinct quantum critical points
• Measurement-induced phase transitions in the toric code
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Topological edge states at Floquet quantum criticality
• Production of lattice gauge-Higgs topological states in measurement-only quantum circuit
• Disentangling transitions in topological order induced by boundary decoherence
• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid
• Protect Measurement-Induced Phase Transition from Noise
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Gauge theory and mixed state criticality
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models

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• Exact, Average, and Broken Symmetries in a Simple Adaptive Monitored Circuit
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Recent progress on disorder-induced topological phases
• Topologically nontrivial multicritical points
• Anomalous Dynamical Scaling at Topological Quantum Criticality