Quantum Hyperuniformity and Quantum Weight

TL;DR

This paper introduces quantum hyperuniformity, a framework extending classical hyperuniformity to quantum fluctuations, to identify quantum phase transitions and characterize phases via the quantum weight in electron systems.

Contribution

It develops the concept of quantum hyperuniformity, classifies quantum phases based on fluctuation scaling, and links quantum weight to gap size, providing new tools for analyzing quantum criticality.

Findings

Quantum hyperuniformity distinguishes different quantum phases.

At criticality, multifractal wave functions cause anomalous scaling.

Quantum weight scales universally with gap size in gapped phases.

Abstract

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-Andre model, we find that gapped, gapless, and localized-critical-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 serves a direct fingerprint of quantum criticality and a practical probe of quantum phase transitions in aperiodic electron systems.