Low energy excitations in bosonic quantum quasicrystals

TL;DR

This paper develops a first-principles effective theory for bosonic quantum quasicrystals, revealing their collective excitations and how they behave across phase transitions.

Contribution

It introduces a generalized elasticity framework that accurately captures Goldstone modes and phononic-phasonic coupling in quantum quasicrystals.

Findings

Dodecagonal and decagonal quasicrystals exhibit isotropic sound speeds.

Octagonal quasicrystals show hybridized excitations with anisotropic sound speeds.

The study discusses excitation mode behavior at phase transitions.

Abstract

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 Goldstone modes. For the dodecagonal and decagonal quasicrystal structures we obtain collective longitudinal and transversal 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 transversal 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.