Pablo López Ríos

Quantum Monte Carlo computations of phase stability, equations of state, and elasticity of high-pressure silica

Silica (SiO2) is an abundant component of the Earth whose crystalline polymorphs play key roles in its structure and dynamics. First principle density functional theory (DFT) methods have often been used to accurately predict properties of silicates, but fundamental failures occur. Such failures occur even in silica, the simplest silicate, and understanding pure silica is a prerequisite to understanding the rocky part of the Earth. Here, we study silica with quantum Monte Carlo (QMC), which until now was not computationally possible for such complex materials, and find that QMC overcomes the failures of DFT. QMC is a benchmark method that does not rely on density functionals but rather explicitly treats the electrons and their interactions via a stochastic solution of Schrödinger’s equation. Using ground-state QMC plus phonons within the quasiharmonic approximation of density functional perturbation theory, we obtain the thermal pressure and equations of state of silica phases up to Earth’s core–mantle boundary. Our results provide the best constrained equations of state and phase boundaries available for silica. QMC indicates a transition to the dense α-PbO2 structure above the core-insulating D” layer, but the absence of a seismic signature suggests the transition does not contribute significantly to global seismic discontinuities in the lower mantle. However, the transition could still provide seismic signals from deeply subducted oceanic crust. We also find an accurate shear elastic constant for stishovite and its geophysically important softening with pressure.

Excitons and biexcitons in symmetric electron-hole bilayers.

Symmetric electron-hole bilayer systems have been studied at zero temperature using the diffusion quantum Monte Carlo method. A flexible trial wave function is used that can describe fluid, excitonic, and biexcitonic phases. We calculate condensate fractions and pair correlation functions for a large number of densities r(s) and layer separations d. At small d we find a one-component fluid phase, an excitonic fluid phase, and a biexcitonic fluid phase, and the transitions among them appear to be continuous. At d=0, excitons appear to survive down to about r(s)=0.5 a.u., and biexcitons form at r(s)>2.5 a.u.

Compression algorithm for multideterminant wave functions.

A compression algorithm is introduced for multideterminant wave functions which can greatly reduce the number of determinants that need to be evaluated in quantum Monte Carlo calculations. We have devised an algorithm with three levels of compression, the least costly of which yields excellent results in polynomial time. We demonstrate the usefulness of the compression algorithm for evaluating multideterminant wave functions in quantum Monte Carlo calculations, whose computational cost is reduced by factors of between about 2 and over 25 for the examples studied. We have found evidence of sublinear scaling of quantum Monte Carlo calculations with the number of determinants when the compression algorithm is used.