Adaptively compressed polarizability operator for accelerating large scale \textit{ab initio} phonon calculations

TL;DR

This paper introduces an adaptively compressed polarizability operator (ACP) method that significantly accelerates large-scale ab initio phonon calculations by reducing computational complexity from (N_e^4) to (N_e^3), applicable to insulators and semiconductors.

Contribution

The paper presents a novel ACP method that adaptively compresses the polarizability operator, enabling more efficient phonon spectrum calculations in large systems.

Findings

Reduces computational complexity from (N_e^4) to (N_e^3)

Applicable to both insulators and small-gap semiconductors

Demonstrated effectiveness on 1D and 2D model problems

Abstract

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.