Exploring quantum quasicrystal patterns: a variational study

TL;DR

This paper investigates the formation of quantum quasicrystals in two-dimensional bosonic systems using a variational mean-field approach, revealing their emergence due to quantum fluctuations and exploring their properties and stability.

Contribution

It introduces a variational method to identify quantum quasicrystal states and analyzes their excitation spectrum and potential super-quasicrystal phases, extending understanding beyond classical models.

Findings

Quantum fluctuations can stabilize quasicrystal configurations in ground states.

Quantum quasicrystals emerge without thermal fluctuations, unlike classical counterparts.

Existence of super-quasicrystals with coexistence of quasicrystalline order and superfluidity.

Abstract

We study the emergence of quasicrystal configurations produced purely by quantum fluctuations in the ground-state phase diagram of interacting bosonic systems. By using a variational mean-field approach, we determine the relevant features of the pair interaction potential that stabilize 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 super-quasicrystals, i.e. supersolid-like quasicrystalline states in which the long-range non-periodic density profile coexist with a non-zero superfluid fraction. Our calculations show 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 work.