Fermionic Anomalies of Finite Symmetries on Lattices

arXiv:2608.12455 · cond-mat.str-el, hep-th, quant-ph · Submitted 2026-08-12 · Read on arXiv

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

Submitted: 2026-08-12

Updated: 2026-09-26

Terminology

• Hilbert Space — 31× in this paper · explained in 2 episodes
• Domain Walls — 4× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Bosonization — 2× in this paper · explained in 2 episodes
• Topological Order — 2× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 4 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes

Sources

• Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems
• Higher symmetries and anomalies in quantum lattice systems
• Disentangling anomaly-free symmetries of quantum spin chains
• Anomaly-free symmetries with obstructions to gauging and onsiteability
• Anomalies on the Lattice, Homotopy of Quantum Cellular Automata, and a Spectrum of Invertible States
• The "Parity" Anomaly On An Unorientable Manifold
• Fermionic SPT phases in higher dimensions and bosonization
• Anomalies and Bosonization
• The Pontrjagin Dual of 3-Dimensional Spin Bordism
• The Pontrjagin Dual of 4-Dimensional Spin Bordism
• Tori, Klein Bottles, and Modulo 8 Parity/Time-reversal Anomalies of 2+1d Staggered Fermions
• Non-invertible bosonic chiral symmetry on the lattice
• Chiral Lattice Gauge Theories from Symmetry Disentanglers
• Exact lattice chiral symmetry in 2d gauge theory
• Anomalies in quantum spin systems and Nielsen-Ninomiya type Theorems
• Fermionic Villain model with exact lattice chiral symmetries
• Infinite-Order Lattice Chiral Anomalies and CPT
• 1+1d Lattice Dirac Fermions from Non-Onsite Vector and Axial Symmetries
• Fermionic Matrix Product Operators and Topological Phases of Matter
• On anomalies and fermionic unitary operators

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