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arXiv · 2509.25316

Topological non-Abelian gauge structures in Cayley-Schreier lattices

Zoltán Guba·Robert-Jan Slager·Lavi K. Upreti·Tomáš Bzdušek
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Abstract

Crystalline constructions known as Cayley-Schreier lattices have been suggested as a platform for realizing arbitrary gauge fields in synthetic crystals with real hopping amplitudes. Here, we reveal that Cayley-Schreier lattices can naturally give rise to implementable lattice systems that incorporate non-Abelian gauge structures transforming into a space-group symmetry. We show that their symmetry sectors can be interpreted as blocks of pseudospin models---some of which correspond to true spinors---that can realize a wealth of different topological invariants in a single setup. We underpin these general results with concrete models and illustrate how they can be implemented in technologically available experimental platforms. Our work sets the stage for a systematic investigation of topological insulators and metals with non-Abelian gauge structures.

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Zoltán Guba, Robert-Jan Slager, Lavi K. Upreti, Tomáš Bzdušek. 2025-09-29. Topological non-Abelian gauge structures in Cayley-Schreier lattices. https://doi.org/10.1038/s41467-026-71401-3

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