### 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.