量子超均匀性与量子权重
Quantum Hyperuniformity and Quantum Weight
AI总结：
该研究通过量子权重揭示量子相变和能隙结构，利用量子超均匀性分类区分不同相态，为无序电子系统中的量子临界性提供新方法。
摘要：
将超均匀性从经典扩展到量子电子系统中的波动，建立了一个框架，通过量子权重识别量子相变并揭示底层的能隙结构。我们通过引入内在量子波动，研究许多体基态的长波波动，通过电荷密度结构因子。尽管零温电荷波动通常因粒子数守恒被抑制，但其长波长标度揭示了定义量子超均匀性类别的不同普遍行为。通过举例 Aubry-Andre 模型，我们发现有隙、无隙和局域临界扩展相通过量子超均匀性类别的区分变得明显。值得注意的是，在临界点，多标度波函数产生异常标度行为。我们进一步表明，在量子超均匀有隙相中，量子权重通过普遍的幂律标度提供间隙大小的定量度量。与经典超均匀性相结合，量子超均匀性成为量子临界性的直接指纹，并成为无序电子系统中量子相变的实用探测器。
英文摘要：
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.
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