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We have performed quantum Monte Carlo (QMC) simulations and densityfunctional theory (DFT) calculations to study the equations of state ofMgSiO$_3$ perovskite (Pv) and post-perovskite (PPv), up to the pressure andtemperature conditions of the base of Earth's lower mantle. The ground stateenergies were derived using QMC and the temperature dependent Helmholtz freeenergies were calculated within the quasi-harmonic approximation and densityfunctional perturbation theory. The equations of state for both phases ofMgSiO$_3$ agree well with experiments, and better than those from generalizedgradient approximation (GGA) calculations. The Pv-PPv phase boundary calculatedfrom our QMC equations of states is also consistent with experiments, andbetter than previous LDA calculations. We discuss the implications for doublecrossing of the Pv-PPv boundary in the Earth.

Equations of state and stability of MgSiO$_3$ perovskite and post-perovskite phases from quantum Monte Carlo simulations