Gauging Modulated Symmetries: Bond Algebras, Higher-Form Symmetries, and Symmetry-Enriched Topological Order

arXiv:2610.10764 · cond-mat.str-el, hep-th · Submitted 2026-10-07 · Read on arXiv

cond-mat.str-el, hep-th

Submitted: 2026-10-07

Updated: 2026-10-07

Terminology

• Anyons — 20× in this paper · explained in 2 episodes
• Topological Order — 16× in this paper · explained in 2 episodes
• Hilbert Space — 10× in this paper · explained in 2 episodes
• Degeneracy — 3× in this paper · explained in 3 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Entanglement — 2× in this paper · explained in 3 episodes
• Symmetry Breaking — 2× in this paper · explained in 3 episodes
• Anyon Condensation — 1× in this paper · explained in 1 episode
• Core — 1× in this paper · explained in 2 episodes
• Entanglement Entropy — 1× in this paper · explained in 2 episodes
• Frustration — 1× in this paper · explained in 2 episodes
• Lifshitz transition — 1× in this paper · explained in 2 episodes
• Multipartite Entanglement — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes

Sources

• What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
• Understanding deconfined quantum critical points from crystalline categorical Landau paradigm
• Generalized $\mathbb{Z}_p$ toric codes as qudit low-density parity-check codes
• Defect Networks for Topological Phases Protected By Modulated Symmetries
• Lieb-Schultz-Mattis constraints from stratified anomalies of modulated symmetries
• Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints
• Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond
• Anomalies of discrete symmetries in various dimensions and group cohomology

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