Quantum quasicrystal patterns from multiple scale potentials: a variational approach

by Alejandro Mendoza-Coto (Universidade Federal de Santa Catarina, Brazil and Max Planck, Dresden, Germany)




We study the emergence of cluster 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 pair
interaction potential stabilising self induced dodecagonal
quasicrystalline states in two dimensions. Unlike their classical
counterpart, in which the interplay between only two wave vectors
determines the stabilisation of these kind of patterns, our results
indicates that in the quantum picture the scenario is more complex due
to the existence of distinct types of quasicrystals depending on the
number of resonant unstable wave vectors in the interaction potential.
Additionally, the quantum cluster quasicrystal patterns are found to
emerge as the ground state with no need of moderate thermal
fluctuations, in this sense the reported phases represent the quantum
analog of the cluster quasicrystal phases well established in the soft
matter field. Moreover, we have also found that depending on the pair
interaction considered quasicrystal phases could exist concomitant
either with a considerable superfluid fraction, giving rise to a
super-quasicrystal phase or even with no global superfluidity,
although maintaining a modest local superfluid fraction, suggesting
the possibility of a self induce quasicrystalline Bose glass phase.

This work is an extension of the work PhDs. Rev. B 105, 134521 (2022).