  The particle-particle random phase approximation (pp-RPA) has been shown to
be capable of describing double, Rydberg, and charge transfer excitations, for
which the conventional time-dependent density functional theory (TDDFT) might
not be suitable. It is thus desirable to reduce the computational cost of
pp-RPA so that it can be efficiently applied to larger molecules and even
solids. This paper introduces an $O(N^3)$ algorithm, where $N$ is the number of
orbitals, based on an interpolative separable density fitting technique and the
Jacobi-Davidson eigensolver to calculate a few low-lying excitations in the
pp-RPA framework. The size of the pp-RPA matrix can also be reduced by keeping
only a small portion of orbitals with orbital energy close to the Fermi energy.
This reduced system leads to a smaller prefactor of the cubic scaling
algorithm, while keeping the accuracy for the low-lying excitation energies.
