AI 中文总结
研究一维晶格上稀疏长程随机键模型，通过概率$p_{ij}= d_{ij}^{-(1+\sigma)}$连接位点对。该模型在无在位无序和相互作用下，小$\sigma$呈现量子混沌谱，大$\sigma$出现局域化本征态，揭示了不同于其他模型的普适类。
AI 中文摘要
本工作表明，仅一维晶格上的稀疏长程随机键就能产生量子混沌谱相关性，并在非相互作用单粒子哈密顿量中驱动局域化转变。该模型是一维环，位点对以概率$p_{ij}= d_{ij}^{-(1+\sigma)}$独立连接，键具有相同单位跳跃且无在位无序。尽管无在位无序和相互作用，小$\sigma$时模型显示具有高斯正交系综（GOE）能级统计的量子混沌谱，大$\sigma$时具有泊松统计的局域化本征态。转变发生在$0.80 \lesssim \sigma_c \lesssim 0.85$范围，远高于平均跳跃分布的可和性阈值（$\sigma=0$）。仅保留伯努利键均值和方差的高斯场论预测阈值在$\sigma=1$，表明更高阶累积量与红外相关。我们的发现暗示了一个不同于幂律随机带状矩阵模型和标准安德森转变的普适类。
英文摘要
This work demonstrates that sparse long-range random bonds on a one-dimensional lattice alone can generate quantum-chaotic spectral correlations and also drive a localization transition in a noninteracting single-particle Hamiltonian. The model is a one-dimensional ring in which each pair of sites is connected independently with a probability $p_{ij}= d_{ij}^{-(1+σ)}$. Each bond carries identical unit hopping and on-site disorder is absent. Despite the absence of on-site disorder and interaction, the model displays quantum chaotic spectra with Gaussian orthogonal ensemble (GOE) level statistics at small $σ$ and localized eigenstates with Poisson statistics at larger $σ$. The transition occurs in the range $ 0.80 \lesssim σ_c \lesssim 0.85$, far above the summability threshold of the mean hopping profile ($σ=0$). A Gaussian field theory retaining only the mean and variance of the Bernoulli bonds instead predicts a threshold at $σ=1$, suggesting that higher cumulants are infrared-relevant. Our findings hint towards a universality class that is distinct from both the power-law random banded matrix model and the standard Anderson transition.
Comments8 (6+2) pages, 4 figures. Comments are welcome
