At the independent particle level, the dielectric polarizability is built from the Lehmann representation considering all possible transitions from the single particle states included in the calculation. However, within the GW approximation this representation is very cumbersome, since the frequency convolution in the self-energy requires the inversion of the Dyson equation for the polarizability evaluated at each transition energy[1]. Many GW implementations overcome this by resorting to the plasmon-pole approximation (PPA) [2,3], a simple model which allows to evaluate the self-energy analytically. Alternative, more accurate full frequency (FF) approaches represent the polarizability in a frequency grid with an affordable number of points, and integrate the self-energy numerically using quadrature

rules [4] or the contour deformation technique [5].

 

In this talk we will introduce the multipole approach (MPA) developed in Ref. [6] to obtain an effective frequency representation of the polarizability. It is based on the Lehmann representation, with complex poles that describe collective excitations. MPA, as a generalization of the PPA case, also provides an analytic expression for the self-energy evaluation, but with an accuracy comparable to FF approaches at a much lower computational cost. We will present results that validate MPA for semiconductors [6] and metals [7], and its combination with the W-av method [8] to accelerate the convergence of GW calculations in both frequency and momentum spaces. We will also discuss the physical interpretation of the MPA poles in a comparison with the main peaks in the EELS spectra of Cu [7].

 

 

References:

 

[1] Mauro Del Ben, et al. PRB 99, 125128 (2019)

[2] MS. Hybertsen and SG. Louie. PRB 34, 5390 (1986)

[3] RW. Godby and RJ. Needs. PRL 62, 1169 (1989)

[4] Fang Liu, et al. J. Comput. Phys. 286, 1 (2015)

[5] Rex W. Godby, et al. PRB 37, 10159 (1988)

[6] Dario A. Leon, et al. PRB 104, 115157 (2021)

[7] Dario A. Leon, et al. PRB 107, 155130 (2023)

[8] Alberto Guandalini, et al. ArXiv: 2304.10810 (2023)