Decorated Defect Construction of Gapless-SPT States

Abstract

Symmetry protected topological (SPT) phases are one of the simplest, yet nontrivial, gapped systems that go beyond the Landau paradigm. In this work, we study an extension of the notion of SPT for gapless systems, namely, gapless symmetry protected topological states. We construct several simple gapless-SPT models using the decorated defect construction, which allow analytical understanding of non-trivial topological features including the symmetry charge under twisted boundary conditions, and boundary (quasi)-degeneracy under open boundary conditions. We also comment on the stability of the gapless-SPT models under symmetric perturbations, and apply small-scale exact diagonalization when direct analytic understanding is not available.

47 pages

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Cited by in corpus (32)

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• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
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• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
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• Symmetry Transmutation and Anomaly Matching
• Gapless higher-order topology and corner states in Floquet systems
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• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
• ${\mathbb{Z}}_2$ gauging and self-dualities of the $XX$ model and its cousins
• Deconfined criticality as intrinsically gapless topological state in one dimension
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Impurity screening by defects in (1+1)$d$ quantum critical systems
• Exploring two dimensional ${\mathbb{Z}}_2$ invariant phases with time reversal symmetry and their transitions with topological operations
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Two-dimensional topological paramagnets protected by ${\mathbb{Z}}_3$ symmetry: Properties of the boundary Hamiltonian
• Critical theories connecting gapped phases with ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry from the duality web
• Anomalous Dynamical Scaling at Topological Quantum Criticality
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• «Anticommuting» ${\mathbb{Z}}_2$ quantum spin liquids