The melting point of silicon in the cubic diamond phase is calculated using the random phase approximation (RPA). The RPA includes exact exchange as well as an approximate treatment of local as well as non-local many body correlation effects of the electrons. We predict a melting temperature of about 1735 K and 1640 K without and with core polarization effects, respectively. Both values are within 3 % of the experimental melting temperature of 1687 K. In comparison, the commonly used gradient approximation to density functional theory predicts a melting point that is 200 K too low, and hybrid functionals overestimate the melting point by 150 K. We correlate the predicted melting point with the energy difference between cubic diamond and the beta-tin phase of silicon, establishing that this energy difference is an important benchmark for the development of approximate functionals. The current results establish that the RPA can be used to predict accurate finite temperature properties and underlines the excellent predictive properties of the RPA for condensed matter.
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