A. Mendoza-Coto | Searcharxiv

arXiv2026

Coexistence of long- and quasi-long range spatial order in 1D quantum quasicrystals

Quasicrystals exhibit long-range positional order without periodicity, arising from multiple incommensurate wave vectors. In self-assembled quasicrystals, the spontaneous breaking of translational invariance gives rise to two Goldstone modes-phonons and phasons-associated with two competing wave vectors. Here, we demonstrate a unique scenario exclusive to quasicrystals: a mechanism that gaps out only one Goldstone mode (associated with one wave vector), while the other remains gapless. In one dimension, this leads to the coexistence of long-range order at the gapped wave vector and quasi-long-range order at the gapless one, due to sustained fluctuations. We show that this phenomenon can be realized using ultracold bosonic atoms in optical cavities.

cond-mat.quant-gas↗

arXiv2021

Exploring quantum quasicrystal patterns: a variational study

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.

cond-mat.quant-gas↗