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 |
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Format: | Artikel |
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. |
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ISSN: | 1098-0121 1550-235X |
DOI: | 10.1103/PhysRevB.89.205117 |