  The pyrochlore lattice involves corner sharing tetrahedra and the resulting
geometric frustration is believed to suppress any antiferromagnetic order for
Mott insulators on this structure. There are nevertheless short-range
correlations which could be vital near the Mott-Hubbard insulator-metal
transition. We use a static auxiliary-field-based Monte Carlo to study this
problem in real space on reasonably large lattices. The method reduces to
unrestricted Hartree-Fock at zero temperature but captures the key magnetic
fluctuations at finite temperature. Our results reveal that increasing
interaction drives the non magnetic (semi) metal to a 'spin disordered' metal
with small local moments, at some critical coupling, and then, through a small
pseudogap window, to a large moment, gapped, Mott insulating phase at a larger
oupling. The spin disordered metal has a finite residual resistivity which
grows with interaction strength, diverging at the upper coupling. We present
the resistivity, optical conductivity, and density of states across the
metal-insulator transition and for varying temperature. These results set the
stage for the more complex cases of Mott transition in the pyrochlore iridates
and molybdates.
