论文标题
Lévy-Rosenzweig-Porter随机矩阵合奏
The Lévy-Rosenzweig-Porter random matrix ensemble
论文作者
论文摘要
在本文中，我们考虑了Rosenzweig-porter（RP）模型的扩展，即Lévy-RP（L-RP）模型，其中广泛分布了非对抗基质矩阵元素，从而提供了更现实的基准，以开发出对相互作用的许多人类相互作用的非体系障碍系统中非癌变扩展（NEE）状态的有效描述。我们提出了一个简单，一般和直观的参数，当杂交是由于分布尾部中的异常大型过渡幅度引起的，允许人们在局部频谱中揭示小带的多重分子结构。这个想法是，可以通过要求站点$ i $和其他支撑集的其他$ n^{d_1} $站点之间的最大矩阵元素的最大矩阵元素的最大矩阵元素的最大值来确定，而支持集的矩阵元素的最大值是相同的$ n^{d_1-1-1} $的相同顺序。该参数产生的分形维度表征了NEE阶段多型波功能的统计以及L-RP集合的整个相图。通过对使用空腔方法获得的局部密度的自洽密度进行彻底研究，并通过数值通过广泛的精确对角线化来确认其预测。
In this paper we consider an extension of the Rosenzweig-Porter (RP) model, the Lévy-RP (L-RP) model, in which the off-diagonal matrix elements are broadly distributed, providing a more realistic benchmark to develop an effective description of non-ergodic extended (NEE) states in interacting many-body disordered systems. We put forward a simple, general, and intuitive argument that allows one to unveil the multifractal structure of the mini-bands in the local spectrum when hybridization is due to anomalously large transition amplitudes in the tails of the distribution. The idea is that the energy spreading of the mini-bands can be determined self-consistently by requiring that the maximum of the matrix elements between a site $i$ and the other $N^{D_1}$ sites of the support set is of the same order of the Thouless energy itself $N^{D_1 - 1}$. This argument yields the fractal dimensions that characterize the statistics of the multifractal wave-functions in the NEE phase, as well as the whole phase diagram of the L-RP ensemble. Its predictions are confirmed both analytically, by a thorough investigation of the self-consistent equation for the local density of states obtained using the cavity approach, and numerically, via extensive exact diagonalizations.
