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Gapless Symmetry-Protected Topological Order, Thomas Scaffidi, Daniel E. Parker, Romain Vasseur

Physics Department Faculty Publication Series

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 …