Motivated by recent experiments and computational results on pyrochlore
iridates, we compare single-particle properties of Y2Ir2O7 obtained from
single-site dynamical mean-field calculations with results within the TRILEX
approximation, where the latter takes non-local correlations into account. Our
calculations are all based on ab-initio calculations within density-functional
theory, and take spin-orbit coupling into account. In order to make the
treatment within TRILEX feasible, we first define a single-band jeff = 1/2
model, by comparing its spectral features within DMFT to a three-band model
that includes both jeff = 1/2 and jeff = 3/2 orbitals. Our calculations show
consistently a paramagnetic metallic phase at small interaction values, and an
insulating antiferromagnetic phase at larger interaction values. The critical
interactions, however, differ between single-site and TRILEX calculations. The
antiferromagnetic phase shows the already predicted all-in/all-out magnetic
ordering. Different to the single-site results, the TRILEX calculation gives
also evidence for the Weyl-semimetal regime in the vicinity of the
metal-insulator transition