Classification of magnetic frustration and metamaterials from topology

We study the relationship between the physics of topology and zero modes in frustrated systems and metamaterials. Zero modes that exist in topological matters are distinct from the ones arising from symmetry breaking. Incidentally, a prominent aspect of frustrated systems and metamaterials also is to harbor such kinds of zero modes in the form of an accidental degeneracy. Taking cues from these two apparently different phenomena, we ask a simple...