Gapped symmetric edges of symmetry-protected topological phases

Symmetry-protected topological (SPT) phases are gapped quantum phases which host symmetry-protected gapless edge excitations. On the other hand, the edge states can be gapped by spontaneously breaking symmetry. We show that topological defects on the symmetry-broken edge cannot proliferate due to th...

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Veröffentlicht in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2014-05, Vol.89 (20), Article 205117
Hauptverfasser: Lu, Yuan-Ming, Lee, Dung-Hai
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Sprache:eng
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Zusammenfassung:Symmetry-protected topological (SPT) phases are gapped quantum phases which host symmetry-protected gapless edge excitations. On the other hand, the edge states can be gapped by spontaneously breaking symmetry. We show that topological defects on the symmetry-broken edge cannot proliferate due to their fractional statistics. A gapped symmetric boundary, however, can be achieved between an SPT phase and certain fractionalized phases by condensing the bound state of a topological defect and an anyon. We demonstrate this by two examples in two dimensions: an exactly solvable model for the boundary between a topological Ising paramagnet and the double-semion model, and a fermionic example about the quantum spin Hall edge. Such a hybrid structure containing both SPT phase and fractionalized phase generally support ground-state degeneracy on a torus.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.89.205117