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.

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

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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