  We investigate the pressure-induced metal-insulator transition from diamond
to beta-tin in bulk Silicon, using quantum Monte Carlo (QMC) and density
functional theory (DFT) approaches. We show that it is possible to efficiently
describe many-body effects, using a variational wave function with an optimized
Jastrow factor and a Slater determinant. Variational results are obtained with
a small computational cost and are further improved by performing diffusion
Monte Carlo calculations and an explicit optimization of molecular orbitals in
the determinant. Finite temperature corrections and zero point motion effects
are included by calculating phonon dispersions in both phases at the DFT level.
Our results indicate that the theoretical QMC (DFT) transition pressure is
significantly larger (smaller) than the accepted experimental value. We discuss
the limitation of DFT approaches due to the choice of the exchange and
correlation functionals and the difficulty to determine consistent
pseudopotentials within the QMC framework, a limitation that may significantly
affect the accuracy of the technique.
