论文标题
具有随机矩阵的多体迁移率的表征
Characterization of many-body mobility edges with random matrices
论文作者
论文摘要
一维相互作用的量子系统中是否可以存在多体迁移率边缘是一个有争议的问题，主要受到有限的系统大小可损坏的数值模拟。我们通过构建一个合并的随机矩阵来研究从混乱到本地化的过渡，该矩阵有两个极端，一个高斯正交集合之一，另一个是来自不同分布的Poisson统计。我们发现，通过固定缩放参数，可以在增加矩阵尺寸$ d \ rightarrow \ infty $的同时存在移动性边缘，具体取决于对角线不相关矩阵的矩阵元素的分布。通过将这些结果应用于随机对角线元件的特定一维隔离量子系统，我们确认存在多体迁移率边缘，并将其与从混合随机矩阵的集合中提取的水平排斥的开始相连。
Whether the many-body mobility edges can exist in a one-dimensional interacting quantum system is a controversial problem, mainly hampered by the limited system sizes amenable to numerical simulations. We investigate the transition from chaos to localization by constructing a combined random matrix, which has two extremes, one of Gaussian orthogonal ensemble and the other of Poisson statistics, drawn from different distributions. We find that by fixing a scaling parameter, the mobility edges can exist while increasing the matrix dimension $D\rightarrow\infty$, depending on the distribution of matrix elements of the diagonal uncorrelated matrix. By applying those results to a specific one-dimensional isolated quantum system of random diagonal elements, we confirm the existence of a many-body mobility edge, connecting it with results on the onset of level repulsion extracted from ensembles of mixed random matrices.
