Fractional Excitations in Non-Euclidean Elastic Plates

We show that minimal-surface non-Euclidean elastic plates share the same low-energy effective theory as Haldane's dimerized quantum spin chain. As a result, such support fractional excitations, which take form of charge-$1/2$ solitons between degenerate states plates, in strong analogy to their counterpart. These exhibit properties similar excitations topological states, including deconfinement and braiding, well unique new features holographic diode-like nonlinear response, demonstrating great potentials for applications mechanical metamaterials.