  We have obtained the equilibrium volumes, bulk moduli, equations of state of
the ferromagnetic cubic $\alpha$ and paramagnetic hexagonal $\epsilon$ phases
of iron in close agreement with experiment using an ab initio dynamical
mean-field theory approach. The local dynamical correlations are shown to be
crucial for a successful description of the ground-state properties of
paramagnetic $\epsilon$-Fe. Moreover, they enhance the effective mass of the
quasiparticles and reduce their lifetimes across the $\alpha \to \epsilon$
transition leading to a step-wise increase of the resistivity, as observed in
experiment. The calculated magnitude of the jump is significantly
underestimated, which points to non-local correlations. The implications of our
results for the superconductivity and non-Fermi-liquid behavior of
$\epsilon$-Fe are discussed.
