论文标题
随机矩阵特征状态的希尔伯特空间几何形状
Hilbert-space geometry of random-matrix eigenstates
论文作者
论文摘要
量子状态多参数家族的几何形状在许多情况下很重要，包括绝热或非绝热量子动力学，量子淬火以及量子临界点的表征。在这里，我们讨论了参数依赖性随机矩阵集合的特征状态的希尔伯特空间几何形状，从而得出了高斯单位合奏的量子几何张量的完整概率分布。我们的分析结果赋予了Fubini-study度量和浆果曲率的确切关节分布函数。我们讨论了征收稳定分布的关系，并将结果与随机磁场中的随机矩阵和电子的数值模拟进行比较。
The geometry of multi-parameter families of quantum states is important in numerous contexts, including adiabatic or nonadiabatic quantum dynamics, quantum quenches, and the characterization of quantum critical points. Here, we discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles, deriving the full probability distribution of the quantum geometric tensor for the Gaussian Unitary Ensemble. Our analytical results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We discuss relations to Levy stable distributions and compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
