论文标题
非依赖性的局部krylov bogoliubov-de Gennes方法：超快速的数值方法，用于大规模不均匀超导体
N-independent Localized Krylov Bogoliubov-de Gennes Method: Ultra-fast Numerical Approach to Large-scale Inhomogeneous Superconductors
论文作者
论文摘要
我们提出了用于大规模不均匀超导体的超快速数值方法，我们称之为局部的Krylov Bogoliubov-De Gennes方法（LK-BDG）。在LK-BDG方法中，局部绿色函数的计算复杂性（用于计算状态和均值场的局部密度）并不取决于系统大小$ n $。自洽计算的计算成本为$ {\ cal o}（n）$，这使我们能够开放一种新的途径，用于用数百万个晶格站点来处理极大的系统。为了显示LK-BDG方法的功能，我们在143806点Penrose penrose准晶晶格上进行了自洽计算，具有涡流的旋转和计算1016064位置的二维二维二维近邻居方形的紧密结合模型，具有许多涡流。我们还证明，只需一个CPU核心就需要不到30秒的时间来计算1亿能量范围的局部密度，该密度在1亿个地点紧密结合模型中。
We propose the ultra-fast numerical approach to large-scale inhomogeneous superconductors, which we call the Localized Krylov Bogoliubov-de Gennes method (LK-BdG). In the LK-BdG method, the computational complexity of the local Green's function, which is used to calculate the local density of states and the mean-fields, does not depend on the system size $N$. The calculation cost of self-consistent calculations is ${\cal O}(N)$, which enables us to open a new avenue for treating extremely large systems with millions of lattice sites. To show the power of the LK-BdG method, we demonstrate a self-consistent calculation on the 143806-site Penrose quasicrystal lattice with a vortex and a calculation on 1016064-site two-dimensional nearest-neighbor square-lattice tight-binding model with many vortices. We also demonstrate that it takes less than 30 seconds with one CPU core to calculate the local density of states with whole energy range in 100-millions-site tight-binding model.
