The Deuterium Hugoniot from Scratch – What Matters in Thermodynamic Sampling with Quantum Monte Carlo*

Density functional theory is the workhorse of ab initio equation of state calculations for warm dense matter, providing a reasonable compromise between accuracy and computational cost.  In dense hydrogen however, several important phase boundaries have been demonstrated to be highly sensitive to the choice of approximate density functional, which has motivated the deployment of more accurate methods like Quantum Monte Carlo (QMC).  One of the most ambitious methods in this vein is coupled electron-ion Monte Carlo (CEIMC), which directly performs thermodynamic sampling using a potential energy surface determined from quantum Monte Carlo. Unfortunately, CEIMC predictions of the deuterium principal Hugoniot disagree significantly with experiment, overshooting the experimentally determined peak compression density by 7% and lower pressure gas gun data by well over 20%. By deriving an equation relating the predicted Hugoniot density to underlying equation of state errors, we show that QMC and other many-body methods can easily spoil the error cancellation properties inherent in the Rankine-Hugoniot relation, and very likely suffer from error addition.  However, QMC’s unique ability to produce systematically improvable results allows it to self-correct to some extent, and thus should make CEIMC and other QMC based methods valuable in this field.