  The Local Density Approximation combined with Dynamical Mean-Field Theory
(LDA+DMFT method) is applied to the study of the paramagnetic and magnetically
ordered phases of hematite Fe$_2$O$_3$ as a function of volume. As the volume
is decreased, a simultaneous 1st order insulator-metal and high-spin to
low-spin transition occurs close to the experimental value of the critical
volume. The high-spin insulating phase is destroyed by a progressive reduction
of the charge gap with increasing pressure, upon closing of which the high spin
phase becomes unstable. We conclude that the transition in Fe$_2$O$_3$ at
$\approx$50 GPa can be described as an electronically driven volume collapse.
