Publication Date
2017
Journal or Book Title
Physical Review X
Abstract
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.
DOI
https://doi.org/10.1103/PhysRevX.7.041048
Volume
7
License
UMass Amherst Open Access Policy
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Funder
UMass SOAR Fund
Recommended Citation
Scaffidi, Thomas; Parker, Daniel E.; and Vasseur, Romain, "Gapless Symmetry-Protected Topological Order" (2017). Physical Review X. 1246.
https://doi.org/10.1103/PhysRevX.7.041048