Quantum

Defining 2-group symmetries on lattices and extracting their anomalies

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Briefings

A new arXiv preprint (2610.37745) defines 2-group symmetries on lattices by linking ordinary and 1-form symmetries via local relations. It extracts anomalies in one spatial dimension using symmetry operations restricted to an interval, constructing explicit qubit actions in d=1,2,3 that realize all cohomological anomaly classes. The study connects higher-group symmetries to microscopic lattice operations.

Key points

• The paper defines a 2-group symmetry class using local relations among symmetry operators on a lattice, which identify the Postnikov class [rho] in H^3(BG, Pi_2) characterizing the mixing between ordinary and 1-form symmetries.
• Anomalies are extracted in one spatial dimension by restricting symmetry operations to an interval and comparing their composition near the endpoints, with explicit qubit actions constructed for d=1,2,3 spatial dimensions.

Context

This research provides a microscopic framework for studying anomalous symmetries by connecting higher-group symmetry and its anomalies to concrete lattice operations, offering a new method to classify and extract anomalies in one spatial dimension.

Limitations

The evidence is a single arXiv preprint (2610.37745v1) with no experimental data, citations, or physical measurements. Results are theoretical and rely on abstract mathematical definitions of symmetry operators and lattice relations, with no confirmation of physical realizability beyond the stated mathematical constructions.

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