  We show that the pressure-induced metal-insulator transition (MIT) in
LaMnO$_3$ is fundamentally different from the Mott-Hubbard transition and is
percolative in nature, with the measured resistivity obeying the percolation
scaling laws. Using the Gutzwiller method to treat correlation effects in a
model Hamiltonian that includes both Coulomb and Jahn-Teller interactions, we
show, One, that the MIT is driven by a competition between electronic
correlation and the electron-lattice interaction, an issue that has been long
debated, and Two, that with compressed volume, the system has a tendency
towards phase separation into insulating and metallic regions, consisting,
respectively, of Jahn-Teller distorted and undistorted octahedra. This tendency
manifests itself in a mixed phase of intermixed insulating and metallic regions
in the experiment. Conduction in the mixed phase occurs by percolation and the
MIT occurs when the metallic volume fraction, steadily increasing with
pressure, exceeds the percolation threshold $v_c \approx 0.29$. Measured
high-pressure resistivity follows the percolation scaling laws quite well,
establishing the percolative nature of conduction, and the temperature
dependence follows the Efros-Shklovskii variable-range hopping behavior for
granular materials.
