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Higgs Condensates are Symmetry-Protected Topological Phases: I. Discrete Symmetries

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arxiv 2211.01376 v2 pith:XQO7RC37 submitted 2022-11-02 cond-mat.str-el cond-mat.supr-conhep-thquant-ph

Higgs Condensates are Symmetry-Protected Topological Phases: I. Discrete Symmetries

classification cond-mat.str-el cond-mat.supr-conhep-thquant-ph
keywords higgsphasephasessymmetrygaugesymmetriesanomalyboundary
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Where in the landscape of many-body phases of matter do we place the Higgs condensate of a gauge theory? On the one hand, the Higgs phase is gapped, has no local order parameter, and for fundamental Higgs fields is adiabatically connected to the confined phase. On the other hand, Higgs phases such as superconductors display rich phenomenology. In this work, we propose a minimal description of the Higgs phase as a symmetry-protected topological (SPT) phase, utilizing conventional and higher-form symmetries. In this first part, we focus on 2+1D $\mathbb Z_2$ gauge theory and find that the Higgs phase is protected by a higher-form magnetic symmetry and a matter symmetry, whose meaning depends on the physical context. While this proposal captures known properties of Higgs phases, it also predicts that the Higgs phase of the Fradkin-Shenker model has SPT edge modes in the symmetric part of the phase diagram, which we confirm analytically. In addition, we argue that this SPT property is remarkably robust upon explicitly breaking the magnetic symmetry. Although the Higgs and confined phases are then connected without a bulk transition, they are separated by a boundary phase transition, which we confirm with tensor network simulations. More generally, the boundary anomaly of the Higgs SPT phase coincides with the emergent anomaly of symmetry-breaking phases, making precise the relation between Higgs phases and symmetry breaking. The SPT nature of the Higgs phase can also manifest in the bulk, e.g., at transitions between distinct Higgs condensates. Finally, we extract insights which are applicable to general SPT phases, such as a 'bulk-defect correspondence' generalizing discrete gauge group analogs of Superconductor-Insulator-Superconductor (SIS) junctions. The sequel to this work will generalize 'Higgs=SPT' to continuous symmetries, interpreting superconductivity as an SPT property.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. There and Back Again: A Gauging Nexus between Topological and Fracton Phases

    cond-mat.str-el 2025-09 unverdicted novelty 7.0

    Gauging the 1-form symmetry in the X-Cube construction produces a web of relations to SPT phases with subsystem and higher-form symmetries plus subsystem symmetry fractionalization in the 3+1D toric code.

  2. PT symmetry-enriched non-unitary criticality

    quant-ph 2025-09 unverdicted novelty 7.0

    PT symmetry enriches non-Hermitian critical points with topological nontriviality, robust edge modes, and a quantized imaginary subleading term in entanglement entropy scaling.

  3. Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems

    cond-mat.str-el 2025-09 unverdicted novelty 6.0

    Derives exact bulk-boundary correspondence allowing extraction of edge-mode degeneracy from bulk entanglement spectrum in critical free-fermion systems of arbitrary dimensions.

  4. Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems

    cond-mat.str-el 2025-09 unverdicted novelty 6.0

    An exact relation is derived between bulk entanglement spectrum and boundary energy spectrum at topological criticality in free-fermion systems, allowing edge-mode degeneracy to be read from bulk data in arbitrary dimensions.

  5. Gauging in superconductors and other electronic systems

    hep-th 2026-04 unverdicted novelty 5.0

    Superconductors are bosonic at low energy yet carry a gravito-magnetic anomaly from fermion parity gauging that forbids trivial massive phases in 3D and 4D.

  6. Varieties of electrically charged physical states in SU(2)$\times$U(1) lattice gauge Higgs theory

    hep-lat 2026-04 unverdicted novelty 5.0

    New orthogonal constructions of charged physical states in SU(2)×U(1) lattice gauge-Higgs theory with a static fermion reveal multiple masses in the charged spectrum.

  7. Universalities of Defects in Quantum Field Theories

    hep-th 2026-05 unverdicted novelty 4.0

    A dissertation synthesizing universal aspects of defect dynamics in QFT through symmetry principles across defect RG flows, effective strings, and quantum gas impurities.