Intrinsically Gapless Topological Phases

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.

6 pages plus appendices

References in corpus (21)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Generalized Global Symmetries
• "Deconfined" quantum critical points
• String order and symmetries in quantum spin lattices
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Averaging Over Narain Moduli Space
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• Anomalies of discrete symmetries in various dimensions and group cohomology
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• The Prediction of a Gapless Topological "Haldane Liquid" Phase in a One-Dimensional Cold Polar Molecular Lattice
• Topological States in a One-Dimensional Fermi Gas with Attractive Interactions
• Classification of abelian spin Chern-Simons theories
• Bosonic Topological Insulators and Paramagnets: a view from cobordisms
• Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in 4d
• Fragility of Symmetry Protected Topological Order on a Hubbard Ladder
• Quantum Criticality in Topological Insulators and Superconductors: Emergence of Strongly Coupled Majoranas and Supersymmetry
• Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions

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• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
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• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
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• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
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