论文标题
无序多体量子系统的地面能量分布
Ground-state energy distribution of disordered many-body quantum systems
论文作者
论文摘要
从低温无序系统的平衡特性到发生自然灾害的均衡性质，研究了极端价值分布。我们这里的重点是无序多体量子系统的基础能量分布。我们得出一个分析表达式，在调整参数后，以高精度重现了我们考虑的系统的基态能量分布。对于某些模型，它与从高斯随机矩阵获得的tracy-widom分布一致。它们包括横向ISING模型，Sachdev-ye模型和PXP模型的随机版本。对于其他系统，例如带有随机耦合的玻色式模型和用于研究多体定位的无序旋转1/2海森贝格链，这些形状与tracy-widom分布不符。我们的分析表达捕获了所有这些分布，因此与Brody分布在大部分频谱中所播放的能量水平相似的最低能级发挥了作用。
Extreme-value distributions are studied in the context of a broad range of problems, from the equilibrium properties of low-temperature disordered systems to the occurrence of natural disasters. Our focus here is on the ground-state energy distribution of disordered many-body quantum systems. We derive an analytical expression that, upon tuning a parameter, reproduces with high accuracy the ground-state energy distribution of the systems that we consider. For some models, it agrees with the Tracy-Widom distribution obtained from Gaussian random matrices. They include transverse Ising models, the Sachdev-Ye model, and a randomized version of the PXP model. For other systems, such as Bose-Hubbard models with random couplings and the disordered spin-1/2 Heisenberg chain used to investigate many-body localization, the shapes are at odds with the Tracy-Widom distribution. Our analytical expression captures all of these distributions, thus playing a role to the lowest energy level similar to that played by the Brody distribution to the bulk of the spectrum.
