Emergent quasicrystals in strongly correlated systems

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.

References in corpus (10)

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Cited by in corpus (9)

• Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics
• Conventional superconductivity in quasicrystals
• Emergent Quasicrystalline Symmetry in Light-Induced Quantum Phase Transitions
• Dual gauge theory formulation of planar quasicrystal elasticity and fractons
• The Fibonacci quasicrystal: case study of hidden dimensions and multifractality
• Fractal ground state of ion chains in periodic potentials
• Quantum frustrated Wigner chains
• Stability of particles in two-dimensional quasicrystals against phasonic perturbations
• Emergence of quasiperiodic behavior in transport and hybridization properties of clean lattice systems