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

A. Mendoza-Coto; M. Grossklags; J. Stefaniak; T. Donner; F. Piazza

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arXiv · 2607.17334

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

A. Mendoza-Coto·M. Grossklags·J. Stefaniak·T. Donner·F. Piazza

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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.

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A. Mendoza-Coto, M. Grossklags, J. Stefaniak, T. Donner, F. Piazza. 2026-07-19. Coexistence of long- and quasi-long range spatial order in 1D quantum quasicrystals. https://arxiv.org/abs/2607.17334

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