论文标题
用指数收敛求解伯特盐方程
Solving the Bethe-Salpeter equation with exponential convergence
论文作者
论文摘要
伯特盐钙方程在理解相关费米的物理学方面起着至关重要的作用，与固体中的光激发以及高能物理学的共振有关。然而，众所周知，很难在数值上控制，通常需要努力以能量尺度和准确性多项式缩放。这使许多有趣的系统无法计算范围。使用Matsubara轴上两个粒子物体的中间表示和稀疏建模，我们开发了一种算法，该算法在$ O（l^8）$中以$ O（l^4）$内存求解了伯特 - 盐的方程政权。我们基准在Hubbard原子和多轨弱偶联极限上进行基准测试，在此我们观察到预期的指数收敛到分析结果。然后，我们展示了现实的杂质问题的方法。
The Bethe-Salpeter equation plays a crucial role in understanding the physics of correlated fermions, relating to optical excitations in solids as well as resonances in high-energy physics. Yet, it is notoriously difficult to control numerically, typically requiring an effort that scales polynomially with energy scales and accuracy. This puts many interesting systems out of computational reach. Using the intermediate representation and sparse modelling for two-particle objects on the Matsubara axis, we develop an algorithm that solves the Bethe-Salpeter equation in $O(L^8)$ time with $O(L^4)$ memory, where $L$ grows only logarithmically with inverse temperature, bandwidth, and desired accuracy, This opens the door for computations in hitherto inaccessible regimes. We benchmark the method on the Hubbard atom and on the multi-orbital weak-coupling limit, where we observe the expected exponential convergence to the analytical results. We then showcase the method for a realistic impurity problem.
