  Recent experiments have shown that sodium, a prototype simple metal at
ambient conditions, exhibits unexpected complexity under high pressure. One of
the most puzzling phenomena in the behaviour of dense sodium is the
pressure-induced drop in its melting temperature, which extends from 1000 K at
~30GPa to as low as room temperature at ~120GPa. Despite significant
theoretical effort to understand the anomalous melting its origins have
remained unclear. In this work, we reconstruct the sodium phase diagram using
an ab-initio-quality neural-network potential. We demonstrate that the
reentrant behaviour results from the screening of interionic interactions by
conduction electrons, which at high pressure induces a softening in the
short-range repulsion. It is expected that such an effect plays an important
role in governing the behaviour of a wide range of metals and alloys.
