Emergent generalized symmetries in ordered phases and applications to quantum disordering

Abstract

We explore the rich landscape of higher-form and non-invertible symmetries that emerge at low energies in generic ordered phases. Using that their charge is carried by homotopy defects (i.e., domain walls, vortices, hedgehogs, etc.), in the absence of domain walls we find that their symmetry defects in $D$-dimensional spacetime are described by $(D-1)$-representations of a $(D-1)$-group that depends only on the spontaneous symmetry-breaking (SSB) pattern of the ordered phase. These emergent symmetries are not spontaneously broken in the ordered phase. We show that spontaneously breaking them induces a phase transition into a nontrivial disordered phase that can have symmetry-enriched (non-)abelian topological orders, photons, and even more emergent symmetries. This SSB transition is between two distinct SSB phases$\unicode{x2013}$an ordinary and a generalized one$\unicode{x2013}$making it a possible generalized deconfined quantum critical point. We also investigate the 't Hooft anomalies of these emergent symmetries and conjecture that there is always a mixed anomaly between them and the microscopic symmetry spontaneously broken in the ordered phase. One way this anomaly can manifest is through the fractionalization of the microscopic symmetry's quantum numbers. Our results demonstrate that even the most exotic generalized symmetries emerge in ordinary phases and provide a valuable framework for characterizing them and their transitions.

16+8 pages, 4+3 figures. v2 & v3: minor changes and added references. v4: published version

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Cited by in corpus (19)

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• The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Twisted Partition Functions as Order Parameters
• Symmetry fractionalization and duality defects in Maxwell theory
• Anomalous continuous symmetries and quantum topology of Goldstone modes
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Higgs Phases and Boundary Criticality
• Intertwined order of generalized global symmetries
• Non-onsite symmetry breaking: topological phase coexistence and criticality
• Non-invertible symmetries of two-dimensional Non-Linear Sigma Models
• Deconfined quantum criticality with internal supersymmetry