Gauge-field-induced duality group in metamaterials

Dualities are mappings that connect seemingly unrelated physical systems, enabling simplification and reinterpretation via duality transformations. However, prior studies have been predominantly limited to one-to-one mappings isomorphic to a $${{\mathbb{Z}}}_{2}$$ group, where self-duality occurs only at a single point at which the lattice maps onto itself under a duality transformation. Here, we extend the duality framework by incorporating gauge fields that modify symmetry representations, constructing more general duality groups, $${{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{2}$$ in two-dimensional systems and $${\left({{\mathbb{Z}}}_{2}\right)}^{6}$$ in three-dimensional systems. We theoretically establish and experimentally validate that such gauge-field-induced duality groups link multiple distinct metamaterials across different symmetry classifications while sharing identical band structures. Notably, in three-dimensional systems, gauge fields promote self-duality from a single point to a set, yielding fourfold degeneracies across the entire Brillouin zone and an eightfold-degenerate double Dirac point. Our work expands duality research and deepens the understanding of hidden symmetries in complex physical systems. Research on dualities is commonly restricted to one-to-one mappings. Here, by incorporating artificial gauge fields, the authors demonstrate 2D and 3D acoustic metamaterials enabling ℤ2 × ℤ2 and (ℤ2)6 duality groups, respectively, where distinct structures share identical band structures, and self-duality gives rise to symmetry-protected high-order degeneracies.