Gapless Symmetry-Protected Topological Order

We introduce exactly solvable gapless quantum systems in d dimensions that support symmetry-protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls “decorated” with dimension (d−...

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Bibliographic Details
Published in:Physical review. X 2017-11, Vol.7 (4), p.041048, Article 041048
Main Authors: Scaffidi, Thomas, Parker, Daniel E., Vasseur, Romain
Format: Article
Language:English
Subjects:
Condensed matter physics
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Critical point
Domain walls
Energy gap
Field theory
Lattice vibration
Metalloids
Perturbation
Symmetry
Topology
Wave functions
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Summary:We introduce exactly solvable gapless quantum systems in d dimensions that support symmetry-protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls “decorated” with dimension (d−1 ) SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, these edge modes are robust against arbitrary symmetry-preserving local perturbations near the edges. In two dimensions, we construct wave functions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.7.041048