Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model

Abstract

Study of boundary phase transition in toric code under cylinder geometry via bulk projective measurement is reported. As the frequency of local measurement for bulk qubits is increased, spin-glass type long-range order on the boundaries emerges indicating spontaneous-symmetry breaking (SSB) of $Z_2$ symmetry. From the lattice-gauge-theory viewpoint, this SSB is a signal of a transition to Higgs phase with symmetry protected topological order. We numerically elucidate the properties of this phase transition in detail, especially its criticality, and give a physical picture using non-local gauge-invariant symmetry operators. Phase transition in the bulk is also studied and its relationship to the boundary transition is discussed.

10 pages, 10 figures, accepted version for Physical Review B

References in corpus (6)

• Generalized Global Symmetries
• Critical properties of the measurement-induced transition in random quantum circuits
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Robustness of a perturbed topological phase
• Lattice Gauge Theory for Condensed Matter Physics: Ferromagnetic Superconductivity as its Example
• Boundary transfer matrix spectrum of measurement-induced transitions

Cited by in corpus (8)

• Robust teleportation of a surface code and cascade of topological quantum phase transitions
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits