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

Abstract: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.

Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2607.17334 [cond-mat.quant-gas]

(or arXiv:2607.17334v1 [cond-mat.quant-gas] for this version)

https://doi.org/10.48550/arXiv.2607.17334 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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