Solving the Bethe-Salpeter equation with exponential convergence
Solving the Bethe-Salpeter equation with exponential convergence
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DOI：
10.1103/physrevresearch.3.033168
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发表时间：
2020-12
影响因子：
4.2
通讯作者：
M. Wallerberger;H. Shinaoka;A. Kauch
中科院分区：
文献类型：
--
作者：
M. Wallerberger;H. Shinaoka;A. Kauch
Bethe-Salpeter方程在理解关联费米子的物理学中起着至关重要的作用，与固体中的光激发以及高能物理中的共振有关。然而，众所周知，数字控制是困难的，通常需要努力与能量尺度和精度进行多项式缩放。这使得许多有趣的系统无法计算。使用松原轴上的两粒子对象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）$时间内以O（L^4）$内存求解Bethe-Salpeter方程，其中L$仅随温度、带宽和所需精度的倒数而数学地增长。我们基准的方法哈伯德原子和多轨道弱耦合限制，在那里我们观察到预期的指数收敛的分析结果。然后，我们展示了一个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.