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We discuss the role of dynamical many-electron effects in the physics of ironand iron-rich solid alloys under applied pressure on the basis of recent abinitio studies employing the dynamical mean-field theory (DMFT). Electroniccorrelations in iron in the moderate pressure range up to 60 GPa are discussedin the first section. DMFT-based methods predict an enhancement of electroniccorrelations at the pressure-induced transition from body-centered cubic (bcc)alpha-Fe to hexagonal close-packed (hcp) epsilon-Fe. In particular, theelectronic effective mass, scattering rate and electron-electron contributionto the electrical resistivity undergo a step-wise increase at the transitionpoint. One also finds a significant many-body correction to the epsilon-Feequation of state, thus clarifying the origin of discrepancies between previousDFT studies and experiment. An electronic topological transition is predictedto be induced in epsilon-Fe by many-electron effects; its experimentalsignatures are analyzed. Next section focuses on the geophysically relevantpressure-temperature regime of the Earth's inner core (EIC) corresponding tothe extreme pressure of 360 GPa combined with temperatures up to 6000 K. Thethree iron allotropes (bcc, hcp and face-centered-cubic) previously proposed aspossible stable phases at such conditions are found to exhibit qualitativelydifferent many-electron effects as evidenced by a strongly non-Fermi-liquidmetallic state of bcc-Fe and an almost perfect Fermi liquid in the case ofhcp-Fe. A recent active discussion on the electronic state and transportproperties of hcp-Fe at the EIC conditions is reviewed in details. We alsodiscuss the impact of a Ni admixture, which is expected to be present in thecore matter. We conclude by outlining some limitation of the present DMFT-basedframework and perspective directions for further development.

Electronic correlations in dense iron: from moderate pressure to Earth's core conditions