  We study the prototype 5d pyrochlore iridate Y2Ir2O7 from first principles
using the local density approximation and dynamical mean-field theory
(LDA+DMFT). We map out the phase diagram in the space of temperature, onsite
Coulomb repulsion U, and filling. Consistent with experiments, we find that an
all-in-all-out ordered insulating phase is stable for realistic values of U.
The trigonal crystal field enhances the magnetic moments of the jeff=1/2
doublet, and strong inter-band correlations are induced by the Coulomb
interaction, which indicates that a three-band description is important. We
demonstrate a substantial band narrowing in the paramagnetic metallic phase and
non-Fermi liquid behavior in the electron/hole doped system originating from
long-lived quasi-spin moments induced by nearly flat bands.
