Approximate exchange-correlation energy from model Green's functions

Density functional theory (DFT) and Green’s function (GF) methods are frequently used together to

model realistic band-structure and photoemission spectra. The strength of DFT comes primarily from

its use of the Kohn-Sham scheme to compute groundstate properties, while GF methods make use of

powerful systematic corrections from many-body perturbation theory. The failures and successes of

DFT and GF methods is still not well understood and is a matter of ongoing research. In this work we

derive a Galitskii-Migdal formula to extract the exchange-correlation (XC) energy from exact and

model Green’s functions. Using our formula we separately analyze the XC contributions associated to

different spectral features of Green’s functions. From the exactly solvable Hubbard dimer, we study the

XC energy contributions from exact and GW quasi-particle and satellite peaks. For the dimer we study

the importance of approximating accurate satellite locations and amplitudes. From our XC energy

formula we motivate and derive a local density approximation (LDA) on the Green’s function directly

and produce the well-known XC energy density from DFT. We motivate alternative approximations

using the density functional formalism.