Correlated many-electron wavefunctions for quantum Monte Carlo calculations of strongly inhomogeneous systems

The quantum many-body problem is among the most challenging in physics. A popular approach is to reduce the problem to the study of a single particle in an effective potential. These one-particle schemes, the most popular of which is density functional theory (DFT) within the local density approximation (LDA), are complemented by more direct methods such as quantum Monte Carlo (QMC), which treat the many interacting particles explicitly. The focus of this thesis is variational Monte Carlo (VMC), a subset of QMC. The thesis consists of two main parts: 1. The accuracy of the trial wavefunctions used determines the quality of VMC calculations. A vital trial function ingredient is the correlation term, and here we investigate one common type based on Bohm and Pines' random phase approximation (RPA) for homogeneous electron gases. We aim to better understand such correlation terms and investigate their extension to inhomogeneous systems. Our analysis explains the success of standard many-electron trial functions combining a correlation term and a Slater determinant of one-electron orbitals from LDA or Hartree-Fock calculations. In addition to clarifying Bohm and Pines' work, we find that our extended RPA theory produces trial wavefunctions slightly better than those derived using the homogeneous RPA. The large computational overhead seems a price worth paying when standard methods (variance optimisation) fail. Some of the features we introduce may also be useful in non-RPA correlation terms. 2. We use standard VMC in conjunction with iterative variance minimisation to study bulk aluminium as a test bed for future work on surfaces. QMC has been used successfully for insulators and semiconductors, but little is known about applying it to metals. LDA calculations for aluminium are reasonably accurate for the bulk modulus and lattice constant. In contrast, the LDA cohesive energy is 1.25 times the experimental value. Due to the large statistical uncertainties the VMC result for the bulk modulus is disappointing, but the VMC cohesive energy is a clear improvement on LDA. In general, we find that QMC is applicable to metals and that the finite-size and other errors are qualitatively no different from those encountered in non-metallic systems. (author)