Low-Energy Excitations in Bosonic Quantum Quasicrystals

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Mechanics

Background:

• Quantum quasicrystals are exotic states of matter with unique, non-periodic atomic arrangements.
• Understanding their low-energy excitations is crucial for predicting their physical properties and potential applications.
• Previous models often lacked the necessary degrees of freedom to accurately describe gapless modes in these systems.

Purpose of the Study:

• To construct a low-energy effective action for bosonic self-organized quantum quasicrystals from first principles.
• To analyze the collective excitations (sound modes) in different quasicrystal structures.
• To investigate the impact of phase and density degrees of freedom on excitation behavior and phase transitions.

Main Methods:

• Developed a generalized elasticity theory to model quantum quasicrystals.
• Incorporated essential phase and conjugate density degrees of freedom.
• Analyzed collective longitudinal and transverse excitations in dodecagonal, decagonal, and octagonal quasicrystal structures.

Main Results:

• Dodecagonal and decagonal quasicrystals exhibit collective excitations with an isotropic speed of sound.
• Octagonal quasicrystals display anisotropic sound speeds due to coupled phononic and phasonic degrees of freedom.
• Identified the behavior of excitation modes at low and high density phase transitions.

Conclusions:

• The generalized elasticity approach accurately describes gapless modes in quantum quasicrystals.
• Structural symmetry dictates the nature of sound propagation (isotropic vs. anisotropic).
• The study provides insights into the stability and dynamics of quantum quasicrystal phases.