Emergent quasicrystals in strongly correlated systems

TL;DR

This paper demonstrates that quasicrystalline structures naturally emerge in strongly correlated electronic systems at irrational filling fractions, revealing new behaviors and potential experimental observations in cold atom setups.

Contribution

It introduces the concept of emergent quasicrystals in strongly correlated systems, linking theoretical models with potential experimental detection.

Findings

Irrationally filled quantum Hall systems form quasiperiodic structures.

Disorder destabilizes these quasicrystals, consistent with quantum Hall plateaux.

Cold Rydberg atom systems can be used to observe emergent quasicrystals.

Abstract

Commensurability is of paramount importance in numerous strongly interacting electronic systems. In the Fractional Quantum Hall effect, a rich cascade of increasingly narrow plateaux appear at larger denominator filling fractions. Rich commensurate structures also emerge, at certain filling fractions, in high temperature superconductors and other electronic systems. A natural question concerns the character of these and other electronic systems at irrational filling fractions. Here we demonstrate that quasicrystalline structures naturally emerge in these situations, and trigger behaviors not typically expected of periodic systems. We first show that irrationally filled quantum Hall systems cross over into quasiperiodically ordered configuration in the thin-torus limit. Using known properties of quasicrystals, we argue that these states are unstable against the effects of disorder, in agreement with the existence of quantum Hall plateaux. We then study analogous physical situations in a system of cold Rydberg atoms placed on an optical lattice. Such an experimental setup is generally disorder free, and can therefore be used to detect the emergent quasicrystals we predict. We discuss similar situations in the Falicov-Kimball model, where known exact results can be used to establish quasicrystalline structures in one and two dimensions. We briefly speculate on possible relations between our theoretical findings and the existence of glassy dynamics and other features of strongly correlated electronic systems.