论文标题
具有有限希尔伯特空间维度的量子系统中的远程级别相关性
Long-range level correlations in quantum systems with finite Hilbert space dimension
论文作者
论文摘要
我们研究具有有限希尔伯特空间的量子系统的光谱统计。我们得出一个定理，即即使是完全可以整合的动力学，由于展开过程，这种系统中的特征级也不能在全球范围内与众不同。我们为$Δ_n$统计量的功率谱提供了一个分析表达式，用于具有级别排斥但独立间距的中间统计模型，并且我们在数值和分析上都表明了结果被展开过程所破坏。然后，我们提供了一个简单的模型来说明这种现象，并通过无序XXZ链上的数字（多体定位的范式模型）和理性Gaudin-Richardson模型（量子集成性的原型模型）通过数字进行测试。
We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated, even in the case of fully integrable dynamics, as a consequence of the unfolding procedure. We provide an analytic expression for the power spectrum of the $δ_n$ statistic for a model of intermediate statistics with level repulsion but independent spacings, and we show both numerically and analytically that the result is spoiled by the unfolding procedure. Then, we provide a simple model to account for this phenomenon, and test it by means of numerics on the disordered XXZ chain, the paradigmatic model of many-body localization, and the rational Gaudin-Richardson model, a prototypical model for quantum integrability.
