The polarizability operator plays a central role in density functional
perturbation theory and other perturbative treatment of first principle
electronic structure theories. The cost of computing the polarizability
operator generally scales as O(Ne4β) where Neβ is the number
of electrons in the system. The recently developed adaptively compressed
polarizability operator (ACP) formulation [L. Lin, Z. Xu and L. Ying,
Multiscale Model. Simul. 2017] reduces such complexity to
O(Ne3β) in the context of phonon calculations with a large basis
set for the first time, and demonstrates its effectiveness for model problems.
In this paper, we improve the performance of the ACP formulation by splitting
the polarizability into a near singular component that is statically
compressed, and a smooth component that is adaptively compressed. The new split
representation maintains the O(Ne3β) complexity, and accelerates
nearly all components of the ACP formulation, including Chebyshev interpolation
of energy levels, iterative solution of Sternheimer equations, and convergence
of the Dyson equations. For simulation of real materials, we discuss how to
incorporate nonlocal pseudopotentials and finite temperature effects. We
demonstrate the effectiveness of our method using one-dimensional model problem
in insulating and metallic regimes, as well as its accuracy for real molecules
and solids.Comment: 32 pages, 8 figures. arXiv admin note: text overlap with
arXiv:1605.0802