Disentangling the Toric Code

arXiv:2609.30363 · cond-mat.str-el, hep-th, math-ph, math.MP, quant-ph · Submitted 2026-09-24 · Read on arXiv

cond-mat.str-el, hep-th, math-ph, math.MP, quant-ph

Submitted: 2026-09-24

Updated: 2026-09-24

Terminology

• Anyons — 18× in this paper · explained in 2 episodes
• Hilbert Space — 9× in this paper · explained in 2 episodes
• Topological Order — 8× in this paper · explained in 2 episodes
• Degeneracy — 6× in this paper · explained in 3 episodes
• Domain Walls — 6× in this paper · explained in 2 episodes
• Entanglement — 5× in this paper · explained in 3 episodes
• Quantization — 4× in this paper · explained in 12 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Bosonization — 2× in this paper · explained in 2 episodes
• Additivity — 1× in this paper · explained in 1 episode
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes

Sources

• TASI 2003 Lectures on Anomalies
• Generalized Symmetries in Condensed Matter
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• General Lieb-Schultz-Mattis type theorems for quantum spin chains
• Anomalies in bosonic SPT edge theories: connection to F-symbols and a method for calculation
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem
• Disentangling anomaly-free symmetries of quantum spin chains
• Classification of locality preserving symmetries on spin chains
• Anomalies of global symmetries on the lattice
• Anomaly-free symmetries with obstructions to gauging and onsiteability
• Higher symmetries and anomalies in quantum lattice systems
• Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems
• Anomalies on the Lattice, Homotopy of Quantum Cellular Automata, and a Spectrum of Invertible States
• Pivot Hamiltonians as generators of symmetry and entanglement
• Bosonic Topological Insulators and Paramagnets: a view from cobordisms
• Disjoint additivity and local quantum physics
• Algebraic locality and non-invertible Gauss laws

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