Gapless Symmetry Protected Topological Order

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Thomas Scaffidi
UC Berkeley
Wednesday, May 3, 2017 - 2:00pm
402 Old LeConte Hall

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 wavefunctions that can be interpreted as critical condensates of domain walls ``decorated'' with (D-1)-dimensional SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT wavefunctions 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, our wavefunctions can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics.