Dual gauge theory formulation of planar quasicrystal elasticity and fractons

Abstract

The elastic description of planar quasicrystals can be formulated as an interplay between two Goldstone fields corresponding to phonon and phason degrees of freedom. We reformulate this description as a gauge theory with one gauge field that is symmetric under an exchange of indices and one that is not. We also show that topological defects in quasicrystals can be succinctly incorporated in the dual description and interpret them as fractonic excitations. Finally, we calculate the static interaction potential between defects in a quasicrystal with fivefold symmetry. This is done in the limit of a small coupling between phonon and phason stresses.