  We present an improved first-principles description of melting under pressure
based on thermodynamic integration comparing Density Functional Theory (DFT)
and quantum Monte Carlo (QMC) treatments of the system. The method is applied
to address the longstanding discrepancy between density functional theory (DFT)
calculations and diamond anvil cell (DAC) experiments on the melting curve of
xenon, a noble gas solid where van der Waals binding is challenging for
traditional DFT methods. The calculations show excellent agreement with data
below 20 GPa and that the high-pressure melt curve is well described by a
Lindemann behavior up to at least 80 GPa, a finding in stark contrast to DAC
data.
