Quasi-Topological Phases of Matter and Topological Protection

Abstract

We discuss systems which have some, but not all of the hallmarks of topological phases. These systems' topological character is not fully captured by a local order parameter, but they are also not fully described at low energies by topological quantum field theories. For such systems, we formulate the concepts of quasi-topological phases (to be contrasted with true topological phases), and symmetry-protected quasi-topological phases. We describe examples of systems in each class and discuss the implications for topological protection of information and operations. We explain why topological phases and quasi-topological phases have greater stability than is sometimes appreciated. In the examples that we discuss, we focus on Ising-type (a.k.a. Majorana) systems particularly relevant to recent theoretical advances and experimental efforts.

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• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Majorana nanowires for topological quantum computation
• Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions
• How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon
• Floquet topological semimetal phases of an extended kicked Harper model
• Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks
• Topological states in a microscopic model of interacting fermions
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Enhanced thermal stability of the toric code through coupling to a bosonic bath
• Doubly Nonlinear Superconducting Qubit
• Degeneracy lifting of Majorana bound states due to electron-phonon interactions
• Globally symmetric topological phase: from anyonic symmetry to twist defect
• Majorana Quasi-Particles Protected by ${\mathbb{Z}}_2$ Angular Momentum Conservation
• Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors
• Non-diagonal anisotropic quantum Hall states
• Modular transformations through sequences of topological charge projections
• Number-conserving interacting fermion models with exact topological superconducting ground states
• Can long-range interactions stabilize quantum memory at nonzero temperature?
• Screening and Topological Order in Thin Superconducting Films
• Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model
• Compass and Kitaev models -- Theory and Physical Motivations
• Non universality of entanglement convertibility
• Gapless Topological Order, Gravity, and Black Holes
• Quantum skyrmion Hall effect
• Quantum phases of a one-dimensional Majorana-Bose-Hubbard model
• Combating quasiparticle poisoning with multiple Majorana fermions in a periodically-driven quantum wire
• Extracting entangled qubits from Majorana fermions in quantum dot chains through the measurement of parity
• Measuring Topological Order
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
• Quantum computing with Octonions
• Ground Subspaces of Topological Phases of Matter as Error Correcting Codes
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing
• Majorana Zero Modes in Nanowires with Combined Triangular and Hexagonal Geometry
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Topologically Induced Fermion Parity Flips in Superconductor Vortices
• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• Microscopic theory of fractional excitations in gapless bilayer quantum Hall states: semi-quantized quantum Hall states
• From Hermitian critical to non-Hermitian point-gapped phases
• Twisted Interferometry
• Geometric Quantum Gates of Non-closed Paths Under Counterdiabatic Driving