Density functional perturbation theory with subspace iteration

Density functional perturbation theory (DFPT) is a useful framework for calculating material responses that can be casted as total energy derivatives with respect to perturbation fields. These responses give access to important properties including the dynamical matrix, dielectric functions, optical properties, electron-phonon coupling, etc. A major advantage of DFPT is circumventing the computational burden of direct methods by replacing DFT supercell calculations, one for each possible perturbation, by a system of coupled linear equations for primitive cells which are solved self-consistently. Nevertheless, for unit cells containing a large number of atoms, solving this linear system becomes a major bottleneck. In this work, we report a new approach to overcome this bottleneck of DFPT, the perturbed Chebyshev-filtered subspace iteration (PCFSI) method, implemented in real space. It allows us to calculate responses of materials in much larger systems than was possible before. Dielectric functions and phonon spectra will be used as examples to demonstrate the impressive power of the PCFSI method.