Hidden-order symmetry-protected topological phases are shown to survive at finite temperature in two dimensions, with Ising- and BKT-class transitions and an intrinsically gapless U(1) variant.
Detection of symmetry- protected topological phases in one dimension,
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Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions
Hidden-order symmetry-protected topological phases are shown to survive at finite temperature in two dimensions, with Ising- and BKT-class transitions and an intrinsically gapless U(1) variant.