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Motivated by recent experiments and computational results on pyrochloreiridates, we compare single-particle properties of Y2Ir2O7 obtained fromsingle-site dynamical mean-field calculations with results within the TRILEXapproximation, where the latter takes non-local correlations into account. Ourcalculations are all based on ab-initio calculations within density-functionaltheory, and take spin-orbit coupling into account. In order to make thetreatment within TRILEX feasible, we first define a single-band jeff = 1/2model, by comparing its spectral features within DMFT to a three-band modelthat includes both jeff = 1/2 and jeff = 3/2 orbitals. Our calculations showconsistently a paramagnetic metallic phase at small interaction values, and aninsulating antiferromagnetic phase at larger interaction values. The criticalinteractions, however, differ between single-site and TRILEX calculations. Theantiferromagnetic phase shows the already predicted all-in/all-out magneticordering. Different to the single-site results, the TRILEX calculation givesalso evidence for the Weyl-semimetal regime in the vicinity of themetal-insulator transition.

Non-local self energies in pyrochlore iridates from ab-initio TRILEX calculations, and their relevance for the Weyl semimetal phase