Algebraic Diagrammatic Construction of the Multichannel Dyson Equation

The multichannel Dyson equation (MCDE) was recently introduced as a new approximation scheme to compute the one-body Green’s function [Riva et al. Phys. Rev. Lett.2023, 131, 216401.] in many-body systems. The physical content of this novel approximation scheme is further clarified by recovering it from (an extended version of) the algebraic diagrammatic construction (ADC) truncation scheme. It is thus demonstrated that the MCDE approximation lies in between the so-called ADC(2) and ADC(3) truncations of the dynamical self-energy. Building on this clarification, the MCDE approximation is benchmarked against ADC(2) and ADC(3) on the periodic one-dimensional Hubbard model with 4-, 6- and 8-site lattices. It delivers an improved treatment over ADC(2) of both the quasiparticle peaks and the so-called satellites in the spectral strength distribution, and performs comparably to or better than ADC(3) in the strong-coupling regime.