A fast low-rank inversion algorithm of dielectric matrix in GW approximation
arxiv(2024)
摘要
The dielectric response function and its inverse are crucial physical
quantities in materials science. We propose an accurate and efficient strategy
to invert the dielectric function matrix. The GW approximation, a powerful
approach to accurately describe many-body excited states, is taken as an
application to demonstrate accuracy and efficiency. We incorporate the
interpolative separable density fitting (ISDF) algorithm with
Sherman–Morrison–Woodbury (SMW) formula to accelerate the inversion process
by exploiting low-rank properties of dielectric function in plane-wave GW
calculations. Our ISDF–SMW strategy produces accurate quasiparticle energies
with O(N_rN_e^2) computational cost (N_e
is the number of electrons and N_r=100–1000N_e is
the number of grid points) with negligible small error of 0.03 eV for both
complex molecules and solids. This new strategy for inverting the dielectric
matrix can be 50× faster than the current state-of-the-art
implementation in BerkeleyGW, resulting in two orders of magnitude speedup for
total GW calculations.
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