Realization of Arbitrary Gauge Fields via Symmetry-Protected Zero Modes

Abstract

Gauge fields are fundamental to modern physics, but prescribed gauge configurations are often difficult to implement in artificial systems. Here, we present a general scheme for realizing arbitrary static $\mathrm{O}(N)$ lattice gauge configurations using symmetry-protected zero modes of sublattice-imbalanced bipartite units. The target $\mathrm{O}(N)$ link on each bond is encoded in the connectivity and strengths of positive microscopic couplings. By decoupling the zero-mode manifold from the remaining modes, the target gauge Hamiltonian forms an exact spectral block of the microscopic tight-binding model rather than a perturbative approximation. We experimentally demonstrate this framework in acoustic crystals through a ${\mathbb{Z}}_2$ quadrupole topological insulator, an $\mathrm{SO}(2)$ Hofstadter model, and an $\mathrm{SO}(3)$ non-Abelian topological insulator. Our results provide a general and accessible route to gauge-field physics in artificial systems.