Auxiliary-Field Quantum Monte Carlo Studies of Pressure-Induced Phase Transitions in Silicon and MnO

Accurate theoretical predictions across structural phase transitions are challenging, as they typically involve different electronic structures on the two sides of the transition. We use the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method---which yields accurate many-body wave functions by means of importance sampled random walks in the space of Slater determinants---to calculate the equation of state near two phase transitions: in Si, from the diamond to metallic $\beta$-tin transition at $\sim 11$ GPa; and in MnO, the volume and magnetic moment collapse at $\sim 100$ GPa. The Si phase transition serves as a test case to study the accuracy of the AFQMC method; the calculated transition pressure is in good agreement with the experiment. Applications to the MnO phase transition will then be presented.