Intrinsically Gapless Topological Phases

TL;DR

This paper introduces a new class of topological phases called intrinsically gapless SPT phases, which are gapless due to anomalous symmetry actions and exhibit unique edge modes and order parameters not possible in gapped systems.

Contribution

It identifies and characterizes intrinsically gapless SPT phases, demonstrating their unique properties and providing a specific realization in a 1D Ising-Hubbard chain.

Findings

Protected edge modes unique to gapless phases

String order parameters forbidden in gapped phases

Constraints on phase diagram upon perturbation

Abstract

Topology in quantum matter is typically associated with gapped phases. For example, in symmetry protected topological (SPT) phases, the bulk energy gap localizes edge modes near the boundary. In this work we identify a new mechanism that leads to topological phases which are not only gapless but where the absence of a gap is essential. These `intrinsically gapless SPT phases' have no gapped counterpart and are hence also distinct from recently discovered examples of gapless SPT phases. The essential ingredient of these phases is that on-site symmetries act in an anomalous fashion at low energies. Intrinsically gapless SPT phases are found to display several unique properties including (i) protected edge modes that are impossible to realize in a gapped system with the same symmetries, (ii) string order parameters that are likewise forbidden in gapped phases, and (iii) constraints on the phase diagram obtained upon perturbing the phase. We verify predictions of the general theory in a specific realization protected by $\mathbb Z_4$ symmetry, the one dimensional Ising-Hubbard chain, using both numerical simulations and effective field theory. We also discuss extensions to higher dimensions and possible experimental realizations.