Quanten-Monte-Carlo - Gesamtenergierechnungen zu strukturellen und dynamischen Eigenschaften von Festkörpern
Quantum Monte Carlo (QMC) methods are a stochastic approach to directly tackle the many-body problem in solids. Especially variational quantum Monte Carlo (VMC) calculations using nonlocal ab initio pseudopotentials offer a way to study many-body effects in real materials systematically, safely founded on Ritz' variational principle 'the lower the energy, the better the wave function'. In this work the method is extended to study dynamical and structural aspects in solids and solid surfaces from first principles, with practical calculations for phonons and the electron-phonon coupling in gallium arsenide (GaAs) and relaxation at the (110) surface of GaAs. Within a frozen phonon scheme, the frequency of an optical phonon is determined with an accuracy of a few meV in very good agreement with experiment. An optical deformation potential approach is chosen for the electron-phonon coupling, showing that the interaction between excited states and distortions of the ion lattice is statistically resolvable within the VMC method. As for the surface systems, taking the boundary condition for the simulation from a finite-layer geometry, the Hamiltonian is cast in a layer-resolved form and evaluated with a two-dimensional Ewald summation technique. The exact cancellation of all jellium contributions to the total energy is ensured. In the trial wave function a confinement term is introduced to compensate for the smoothing effect of the Jastrow factor. A realistic surface model of GaAs(110) is compared with the ideal geometry for different system sizes, showing a consistent finite size dependence of the total energy per atom. With the resulting optimal wave function further surface specific information is extracted to further analyze the many-body effects at solid surfaces.