Interaction-Induced Quasicrystalline Order: Emergence of Quasi-Solid and Quasi-Supersolid Phases

TL;DR

This paper demonstrates that quasiperiodic long-range interactions in quantum systems can induce stable quasicrystalline and supersolid phases without external quasiperiodic potentials, revealing a new mechanism for ordered quantum matter.

Contribution

It introduces a novel interaction-driven mechanism for stabilizing quasicrystalline and supersolid phases in quantum systems without external quasiperiodic potentials.

Findings

Identification of stable incompressible plateaus at irrational densities.

Observation of sharp incommensurate Bragg peaks indicating quasicrystalline order.

Discovery of a quasi-supersolid phase with both density order and superfluidity.

Abstract

Deterministic quasiperiodicity in quantum systems has long been associated with localization, criticality, or glassy behavior, and has therefore been believed to suppress long-range order rather than stabilize it. Here we demonstrate the opposite: quasiperiodicity in interactions--without any quasiperiodic potential, disorder, or geometric modulation--can generate coherent, ordered quantum phases. We study hard-core bosons in one dimension with quasiperiodic long-range interactions, V_{ij}=V_0 \cos(\pi \alpha i)\cos(\pi \alpha j), where n=\alpha=(\sqrt{5}-1)/2 is the inverse golden ratio. Using large-scale path-integral quantum Monte Carlo simulations, we uncover thermodynamically stable incompressible plateaus at irrational densities tied to Fibonacci ratios. These plateaus exhibit sharp incommensurate Bragg peaks, signaling an emergent quasi-solid with long-range quasicrystalline density order. More strikingly, at nearby fillings and interaction strengths, we identify a quasi-supersolid phase that supports both Fibonacci density ordering and finite superfluid density--demonstrating that interaction-induced quasiperiodicity can stabilize supersolid coherence. Our results establish a new mechanism for realizing ordered quasicrystalline quantum matter, and provide realistic guidance for implementation in Rydberg atom arrays, multimode cavity-QED systems, and trapped-ion quantum simulators.