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, $V_{ij}=V_{0}cos\left(\pi \alpha i\right)cos\left(\pi \alpha j\right)$, where $\alpha =(\sqrt{5}-1)/2$ 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 quasisolid with long-range quasicrystalline density order. More strikingly, at nearby fillings and interaction strengths, we identify a quasisupersolid phase that supports both Fibonacci density ordering and finite superfluid density—demonstrating that interaction-induced quasiperiodicity can stabilize supersolid coherence. Our results establish a mechanism for realizing ordered quasicrystalline quantum matter, and suggest possible routes toward implementation in engineered platforms such as multimode cavity-QED systems, programmable Rydberg arrays, and trapped-ion quantum simulators.

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• Quantum phase transitions
• Superfluidity
• Quantum fluids & solids
• Supersolids
• Quantum Monte Carlo