Low-Energy Excitations in Bosonic Quantum Quasicrystals

We present the first principles construction of the low energy effective action for bosonic self-organized quantum quasicrystals. Our generalized elasticity approach retains the appropriate number of phase and corresponding conjugate density degrees of freedom required for a proper description of the gapless modes. For the dodecagonal and decagonal quasicrystal structures we obtain collective longitudinal and transverse excitations with an isotropic speed of sound. Meanwhile, for the octagonal structure, the coupling between phononic and phasonic degrees of freedom leads in turn to hybridization of the latter with the condensate sound mode, producing collective excitations with a longitudinal and transverse component and an anisotropic speed of sound. Finally, we discuss the fate of each excitation mode at the low and high density phase transitions limiting the quantum quasicrystal phase.