Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model

Abstract

We examine the condensation and confinement mechanisms exhibited by a deformed toric code model proposed in [Castelnovo and Chamon, Phys. Rev. B, 2008]. The model describes both sides of a phase transition from a topological phase to a trivial phase. Our findings reveal an unconventional confinement mechanism that governs the behavior of the toric code excitations within the trivial phase. Specifically, the confined magnetic charge can still be displaced without any energy cost, albeit only via the application of non-unitary operators that reduce the norm of the state. This peculiar phenomenon can be attributed to a previously known feature of the model: it maintains the non-trivial ground state degeneracy of the toric code throughout the transition. We describe how this degeneracy arises in both phases in terms of spontaneous symmetry breaking of a generalized (1-form) symmetry and explain why such symmetry breaking is compatible with the trivial phase. The present study implies the existence of subtle considerations that must be addressed in the context of recently posited connections between topological phases and broken higher-form symmetries.

19 pages plus 13 pages of appendices, 8 figures, Submission to Scipost, v2: references added, typos fixed, added comments on 't Hooft anomalies, v3: new section about more general models

References in corpus (19)

• Non-Abelian Anyons and Topological Quantum Computation
• Generalized Global Symmetries
• Condensate induced transitions between topologically ordered phases
• Topological Order and Conformal Quantum Critical Points
• Repeated Quantum Error Detection in a Surface Code
• Generalized Symmetries in Condensed Matter
• A classification of symmetry enriched topological phases with exactly solvable models
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems
• A quantum topological phase transition at the microscopic level
• Gapless Coulomb state emerging from a self-dual topological tensor-network state
• Dynamics at and near conformal quantum critical points
• Exact emergent higher-form symmetries in bosonic lattice models
• Topological fracton quantum phase transitions by tuning exact tensor network states
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• Simplified Transfer Matrix Approach in the Two-Dimensional Ising Model with Various Boundary Conditions
• Global entanglement in a topological quantum phase transition
• Topological line in frustrated Toric code models
• Foliated order parameter in a fracton phase transition

Cited by in corpus (9)

• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Playing nonlocal games across a topological phase transition on a quantum computer
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Decoherence through Ancilla Anyon Reservoirs
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing
• Edge Theories for Anyon Condensation Phase Transitions
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits
• Higher-form entanglement asymmetry and topological order