Quantum Monte Carlo for Materials at High Pressures

Ronald E. Cohen
Carnegie Institution for Science, Washington, D.C. USA
and
University College London, UK

In spite of the great success of density functional theory (DFT), the only justification for the use of approximate density functionals is by comparisons with experiments. In many cases, especially for new materials or under extreme conditions, there are few or no experiments available. Some systems are known to be problematic for DFT, such as molecules or materials that are highly correlated or have important dispersion forces. In addition, even in ordinary materials sometimes accuracy greater than can be provided by DFT is required, such as in geophysics. Diffusion Monte Carlo (DMC) gives the ground state energy with no uncontrolled approximations, although practical calculations typically use pseudopotentials and the fixed node approximation for the many-body wave function. We have applied DMC using the casino and qmcpack codes to high pressure problems including developing a fundamental high pressure scale using cubic Boron Nitride, and constraining the equations of state and phase transitions in SiO2 and MgSiO3. DMC gives the ground state energies accurately, but other properties are difficult to obtain. Also, solids with multi-determinantal ground states remain problematic. Using Dynamical Mean Field Theory (DMFT) with DFT we can study materials with strong correlations, and obtain spectral and optical properties, etc., at finite electronic temperatures. We solve self-consistently for the correlated subsystem and for the crystal. The quantum impurity problem is solved using continuous time quantum Monte Carlo with a hybridization function and impurity levels from the crystal. The crystal problem is solved using DFT with an additional self-energy from the quantum impurity problem. There is multi-loop self-consistency. Using Kristjan Haule's DFT/DMFT code, we have predicted metallisation in FeO at high pressures and temperatures, studied Fe-superconductors and other systems under pressure.