Gapless Symmetry Protected Topological Order

TL;DR

This paper introduces exactly solvable gapless quantum systems with symmetry-protected topological edge modes, revealing novel critical phases with robust edge states despite the absence of a bulk gap.

Contribution

It presents a new class of gapless SPT systems with exact solutions, combining field theory and lattice results to explore their edge modes and critical properties.

Findings

Edge modes can be gapless or symmetry-broken.

Edge states are robust against local perturbations.

Constructed wavefunctions exhibit diffusive bulk and ballistic edge dynamics.

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 wavefunctions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics.