trailTopological order can distinguish phases of matter that have identical symmetry realization
Phases of matter with the same symmetry-breaking pattern can always be connected without a phase transition
Topological invariants of a gapped phase cannot change without closing the energy gap or crossing a phase transition
atomic
Fractional quantum Hall states at different filling fractions are distinct phases with identical symmetry realization
atomic
Topological order or vortex statistics sharply distinguish the color-flavor-locked phase from superfluid hadronic matter
Aharonov-Bohm phases of test quarks around superfluid vortices distinguish Higgs from confining regimes
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Superfluid vortices can connect continuously between hadronic matter and color-flavor-locked quark matter
Symmetry breaking on vortex worldsheets can distinguish Higgs and confining regimes without a bulk phase transition
The phase of a vortex-line operator linking an electric Wilson line distinguishes Higgs from confining regimes
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Topological order can distinguish phases of matter that have identical symmetry realization
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