Quantum Monte Carlo Equations of State of $\alpha$- and $\beta$-Magnesium Silicate*

The 410 km seismic discontinuity in Earth's mantle is ascribed to the $\alpha$ to $\beta$-(Mg,Fe)$_2$SiO$_4$ phase transformation. Considering Mg-endmembers, density functional theory (DFT) predictions within LDA and GGA disagree on the phase boundary by 50\% [1]. Quantum Monte Carlo (QMC) offers a route to avoid the approximation of the exchange-correlation potential in DFT and provide a benchmark for the phase boundary, elastic moduli, and thermodynamic properties. Zero point and thermal contributions are included by using DFT linear response within the quasiharmonic approximation. Preliminary results indicate the QMC phase relations and bulk moduli are in reasonable agreement with experiment. \\[4pt] [1] Y. Yu, Z. Wu., R. M. Wentzcovitch, Earth Planet. Sci. Lett. 273, 115 (2008).