论文标题
在一个维度上的无序和相互作用的几个粒子系统的分裂和诱导算法
A Divide-and-Conquer Algorithm for Disordered and Interacting Few-Particle Systems in One Dimension
论文作者
论文摘要
我们提出了一种算法来解决非常大的一维无序和相互作用的几个粒子系统。我们的方法利用了真实空间中特征函数的局部性质，以实现总系统尺寸$ l $的线性缩放。这使我们可以解决具有多达十亿个地点的不同类型的单粒子系统的所有征函数。基于这项技术，我们收集了非常详细的本征函数性能的直方图，例如定位长度或参与比与其能量的函数。这些直方图揭示了令人惊讶的丰富的精细结构，我们的起源是我们讨论的。我们还将算法应用于单个粒子问题，并非所有本征函数均已定位并显示如何诊断出来。最后，我们将算法扩展到存在障碍存在的两粒子问题，并证明我们的算法非常适合分析相互作用对波形的影响。
We present an algorithm to solve very large one-dimensional disordered and interacting few-particle systems. Our approach exploits the localized nature of the eigenfunctions in real space to achieve a linear scaling with the total system size $L$. This allows us to solve for all eigenfunctions of single-particle systems with different types of disorder up to one billion sites. Based on this technology we collect very detailed histograms of properties of eigenfunctions, such as the localization length or the participation ratio as a function of their energy. These histograms reveal surprisingly rich fine structures, whose origins we discuss. We also apply the algorithm to single particle problems where not all eigenfunctions are localized and show how this is diagnosed. Finally we extend the algorithm to interacting two-particle problems in the presence of disorder and demonstrate that our algorithm is well suited to analyze the effect of interactions on wavefunctions.
