Gapped symmetric edges of symmetry protected topological phases

Abstract

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 topological Ising paramagnet and 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 torus.

6 pages, 2 figures, published version

References in corpus (6)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• A classification of symmetry enriched topological phases with exactly solvable models
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Weak symmetry breaking in two dimensional topological insulators

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