  We present a comprehensive investigation of the electrical and thermal
conductivity of iron under high pressures at ambient temperature, employing the
real-time formulation of time-dependent density functional theory (RT-TDDFT).
Specifically, we examine the influence of a Hubbard correction (+\textit{U}) to
account for strong electron correlations. Our calculations based on RT-TDDFT
demonstrate that the evaluated electrical conductivity for both high-pressure
body-centered cubic (BCC) and hexagonal close-packed (HCP) iron phases agrees
well with experimental data. Furthermore, we explore the anisotropy in the
thermal conductivity of HCP iron under high pressure, and our findings are
consistent with experimental observations. Interestingly, we find that the
incorporation of the +\textit{U} correction significantly impacts the ground
state and linear response properties of iron at pressures below 50 GPa, with
its influence diminishing as pressure increases. This study offers valuable
insights into the influence of electronic correlations on the electronic
transport properties of iron under extreme conditions.
