Exploring quantum quasicrystal patterns: A variational study

We study the emergence of quasicrystal configurations in the ground-state phase diagram of bosonic systems interacting through pair potentials of Lifshitz???s type. By using a variational mean-field approach, we determine the relevant features of the corresponding potential interaction kind stabilizing such quasicrystalline states in two dimensions. Unlike their classical counterpart, in which the interplay between only two wave vectors determines the resulting symmetries of the solutions, the quantum picture relates in a more complex way to the instabilities of the excitation spectrum. Moreover, the quantum quasicrystal patterns are found to emerge as the ground state with no need of moderate thermal fluctuations. The study extends to the exploration of the excitation properties and the possible existence of superquasicrystals, i.e., supersolidlike quasicrystalline states in which the long-range nonperiodic density profile coexists with a nonzero superfluid fraction. Our calculations suggest that, in an intermediate region between the homogeneous superfluid and the normal quasicrystal phases, these exotic states indeed exist at zero temperature. Comparison with full numerical simulations provides a solid verification of the variational approach adopted in this paper.

Automated summary

We study the emergence of quasicrystal configurations in bosonic systems interacting through Lifshitz's pair potentials. Utilizing a variational mean-field approach, we determine the relevant characteristics of the potential interaction which stabilize quasicrystalline states in two dimensions. Unlike classical counterparts, the quantum picture relates to the instabilities of the excitation spectrum in a more complex way. Additionally, quantum quasicrystal patterns are found to be the ground state without thermal fluctuations. The study extends to exploring the excitation properties and the possibility of superquasicrystals, where a nonperiodic density profile coexists with a nonzero superfluid fraction. The calculations suggest that these exotic states exist at zero temperature in an intermediate region. The variational approach used in this paper is verified through comparison with full numerical simulations.