Quantum Monte Carlo Calculation for the Equation of State of MgSiO$_{3}$ perovskite at high pressures*

Magnesium silicate (MgSiO$_{3})$ is among the most abundant minerals in the Earth's mantle. Its phase behavior under high pressure has important implications for the physical properties of deep Earth and the core-mantle boundary. A number of experiments and density functional theory calculations have studied perovskite and its transition to the post-perovskite phase. Here, we present our initial work on the equation of state of perovskite at pressures up to 200 GPa using quantum Monte Carlo (QMC), a benchmark ab initio method. Our QMC calculations optimize electron correlation by using a Slater-Jastrow type wave function~with a single determinant comprised of single-particle orbitals extracted from fully converged DFT calculations.~The equation of state obtained from QMC calculations agrees with experimental data.