Interacting Topological Phases
Strongly interacting electrons can form incompressible liquids with fractionally charged excitations. Explore each principle from mathematical definition to physical evidence and limitations.
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Concept 27Fractional quantum Hall effectStrongly interacting electrons can form incompressible liquids with fractionally charged excitations.Concept 28Anyons and braid statisticsIn two spatial dimensions, exchanges can have richer statistics than bosons or fermions.Concept 29Topological order and long-range entanglementSome many-body phases cannot be characterized by local symmetry-breaking order parameters.Concept 30Toric code and stabilizersLocal commuting operators can produce a globally entangled ground space.Concept 31Majorana zero modesA Majorana operator is its own Hermitian conjugate and can describe a zero-energy boundary mode in a superconducting model.Concept 32Kitaev chain and topological superconductivityA simple one-dimensional p-wave superconducting model can host unpaired Majorana end modes.Concept 33Non-Abelian braiding and encoded gatesExchanging non-Abelian anyons can rotate a protected degenerate subspace.Concept 34Symmetry-protected topological phasesSome short-range-entangled phases become distinct only when a symmetry is enforced.