Homogeneous Holographic Viscoelastic Models & Quasicrystals

We show that the field theories dual to the homogeneous holographic models with spontaneously broken translations display several distinctive properties of quasicrystals, aperiodic crystals with long-range order (e.g. incommensurate charge density waves). This interpretation suggests that the longitudinal diffusive mode, observed in the spectrum of excitations of these systems, is the diffusive Goldstone boson typical of quasicrystals -- the phason. Moreover, following this idea, and using the effective field theory formalism for Goldstone modes in dissipative systems, we are able to derive the universal phase relaxation found in these holographic models in presence of a small source of explicit breaking (pseudo-spontaneous regime).