自适应压缩极化率算子用于加速大规模从头计算声子计算
Adaptively compressed polarizability operator for accelerating large scale \textit{ab initio} phonon calculations
AI总结：
本文提出一种自适应压缩极化率算子方法，将声子计算复杂度从O(N_e^4)降至O(N_e^3)，适用于绝缘体和半导体的声子谱计算。
摘要：
基于第一性原理电子结构理论的声子计算，如Kohn-Sham密度泛函理论，在物理、化学和材料科学中有广泛应用。第一性原理声子计算的计算成本通常随电子数N_e呈O(N_e^4)增长。本文开发了一种新方法，将计算完整动力学矩阵和声子谱的复杂度降至O(N_e^3)。关键概念是自适应压缩极化率算子，以适应由于原子配置变化引起的势扰动。这种自适应压缩极化率算子（ACP）允许准确计算声子谱。复杂度的降低仅弱依赖于能隙大小，该方法适用于绝缘体和具有小能隙的半导体。通过一维和二维模型问题验证了该方法的有效性。
英文摘要：
Phonon calculations based on first principle electronic structure theory, such as the Kohn-Sham density functional theory, have wide applications in physics, chemistry and material science. The computational cost of first principle phonon calculations typically scales steeply as $\mathcal{O}(N_e^4)$, where $N_e$ is the number of electrons in the system. In this work, we develop a new method to reduce the computational complexity of computing the full dynamical matrix, and hence the phonon spectrum, to $\mathcal{O}(N_e^3)$. The key concept for achieving this is to compress the polarizability operator adaptively with respect to the perturbation of the potential due to the change of the atomic configuration. Such adaptively compressed polarizability operator (ACP) allows accurate computation of the phonon spectrum. The reduction of complexity only weakly depends on the size of the band gap, and our method is applicable to insulators as well as semiconductors with small band gaps. We demonstrate the effectiveness of our method using one-dimensional and two-dimensional model problems.
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