Extending hyperuniformity from classical to quantum fluctuations in electron systems yields a framework that identifies quantum phase transitions and reveals underlying gap structures through the quantum weight. We study long-wavelength fluctuations of many-body ground states through the charge-density structure factor by incorporating intrinsic quantum fluctuations into hyperuniformity. Although charge fluctuations at zero temperature are generally suppressed by particle-number conservation, their long-wavelength scaling reveals distinct universal behaviors that define quantum hyperuniformity classes. By exemplifying the Aubry-André model, we find that gapped and gapless phases, as well as localized, critical, and extended phases are sharply distinguished by the quantum hyperuniformity classes. Notably, at the critical point, multifractal wave functions generate anomalous scaling behavior. We further show that, in quantum-hyperuniform gapped phases, the quantum weight provides a quantitative measure of the gap size through a universal power-law scaling. Along with classical hyperuniformity, quantum hyperuniformity class serves a direct fingerprint of quantum criticality and a practical probe of quantum phase transitions in aperiodic electron systems.

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• Localization
• Quantum geometry
• Quantum phase transitions
• 1-dimensional systems
• Quasicrystals
• Tight-binding model