Exploring quantum quasicrystal patterns: A variational study

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