Anomaly-Free Symmetries with Obstructions to Gauging and Onsiteability
Abstract
We present counterexamples to the lore that symmetries that cannot be gauged or made on site are necessarily anomalous. Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently coupled to background or dynamical gauge fields or disentangled to a tensor product of on-site operators. These symmetries are nevertheless anomaly-free in the sense that they admit symmetric, gapped Hamiltonians with unique, invertible ground states. We show that symmetries of this kind are characterized by an index [ω]∈H^{2}(G,Q_{+}), where Q_{+} is the multiplicative group of positive rational numbers labeling one-dimensional quantum cellular automata.
Fields of Study & Subjects
Quasicrystal Structures and Properties
Black Holes and Theoretical Physics
Theoretical and Computational Physics
Publication details
- Journal / source
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Volume
- 136
- Issue
- 21
- Pages
- 216602–216602
- Publication date
- 20 January 2026
- Language
- EN