Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications

Abstract

We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d boundary state of 4d SPT states involving 1-form symmetries can be either a gapless photon phase (quantum electrodynamics) or gapped topological order enriched by 1-form symmetries, namely the loop excitations of these topological orders carry nontrivial 1-form symmetry charges. This study also serves the purpose of diagnosing anomaly of 3d states of matter. Connection between SPT states with 1-form symmetries and condensed matter systems such as quantum dimer models at one lower dimension will also be discussed. Whether a quantum dimer model can have a trivial gapped phase or not depends on the nature of its corresponding bulk state in one higher dimension.

10 pages, 1 figure

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Cited by in corpus (11)

• Universal Features of Higher-Form Symmetries at Phase Transitions
• Exact emergent higher-form symmetries in bosonic lattice models
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Theory of oblique topological insulators
• Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors
• Entanglement Spectrum Resolved by Loop Symmetries