Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models

Abstract

We extensively study long-time dynamics and fate of topologically-ordered state in toric code model evolving through projective measurement-only circuit. The circuit is composed of several measurement operators corresponding to each term of toric code Hamiltonian with magnetic-field perturbations, which is a gauge-fixed version of a (2+1)-dimensional gauge-Higgs model. We employ a cylinder geometry with distinct upper and lower boundaries to classify stationary states after long-time measurement dynamics. The appearing stationary states depend on measurement probabilities for each measurement operator. The Higgs, confined and deconfined phases emerge in the time evolution by the circuit. We find that both Higgs and confined phases are separated from the deconfined phase by topological entanglement entropy. We numerically clarify that both Higgs and confined phases are characterized by a long-range order on the boundaries accompanying edge modes, and they shift with each other by a crossover reflecting properties in the bulk phase diagram.

arXiv commentVersion to appear in Phys. Rev. B. 10 pages, 9 figures

References in corpus (47)

• Fault-tolerant quantum computation by anyons
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Generalized Global Symmetries
• Improved Simulation of Stabilizer Circuits
• Suppressing quantum errors by scaling a surface code logical qubit
• Measurement-based quantum computation
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Measurement-driven entanglement transition in hybrid quantum circuits
• Theory of the phase transition in random unitary circuits with measurements
• Measurement-induced criticality in random quantum circuits
• Random Quantum Circuits
• Unitary-projective entanglement dynamics
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Dynamical purification phase transitions induced by quantum measurements
• Critical properties of the measurement-induced transition in random quantum circuits
• Generalized Symmetries in Condensed Matter
• Stabilizer Formalism for Operator Quantum Error Correction
• Entanglement transition from variable-strength weak measurements
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Entanglement phase transitions in measurement-only dynamics
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits
• Entanglement Transitions from Holographic Random Tensor Networks
• Low-energy effective theory of the toric code model in a parallel field
• Measurement Protected Quantum Phases
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Robustness of a perturbed topological phase
• Topological multicritical point in the Toric Code and 3D gauge Higgs Models
• Quantum criticality under decoherence or weak measurement
• Topological order and criticality in (2+1)D monitored random quantum circuits
• Long-range entanglement from measuring symmetry-protected topological phases
• Entanglement Negativity at Measurement-Induced Criticality
• Phase diagram of the toric code model in a parallel magnetic field
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• Transport and entanglement growth in long-range random Clifford circuits
• Measurement induced entanglement transition in two dimensional shallow circuit
• Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits
• Measurement-induced phase transitions in the toric code
• Boundary transfer matrix spectrum of measurement-induced transitions
• Production of lattice gauge-Higgs topological states in measurement-only quantum circuit
• Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
• Phase transition and evidence of fast-scrambling phase in measurement-only quantum circuit
• Interplay between lattice gauge theory and subsystem codes
• The functional form of open Wilson lines in gauge theories coupled to matter

Cited by in corpus (4)

• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits