  We use computationally simple neutral pseudo-atom (`average atom') one-center
density functional theory (DFT) and standard N-center DFT-Molecular Dynamics
simulations to elucidate liquid-liquid phase transitions (LPTs) in supercooled
liquid silicon at 1200K ,and also in silicon under warm-dense matter conditions
up to 11604k (1 eV). An ionization-driven transition and three LPTs including
the known LPT near 2.5 g/cm$^3$ are found. They are robust even to 1 eV. The
pair distributions functions, pair potentials, electrical conductivities, and
compressibilites are reported. The LPTs are elucidated within a Fermi liquid
picture of electron scattering at the Fermi energy that complements the usual
transient covalent bonding picture.
