Full configuration interaction quantum Monte Carlo (FCIQMC) is a method for stochastically
solving the many-body Schrödinger equation and has proven to be extremely accurate when
applied to a range of model systems and molecular systems. In this thesis, we showcase two
bodies of work that employ FCIQMC to study solid-state systems. Firstly, we demonstrate
the use of FCIQMC in a single-particle basis of plane waves to study the ground states of
real solids, with a periodic lattice of nuclei represented by Trail-Needs pseudopotentials.
We demonstrate that FCIQMC can produce ground state energies comparable to diffusion
Monte Carlo in a 2 × 2 × 2 aluminium supercell, and discuss the challenges extending this
functionality to larger systems. Secondly, we experiment with calculating properties beyond
the ground state. In particular, we focus on spectral properties of the uniformelectron gas. We
develop two different approaches for evaluating the quasiparticle energy and effective mass
—the density dependence of the latter has been a subject of recent theoretical controversy.
For the range of densities studied, we find the effective mass to decrease monotonically as
density decreases, in agreement with prior diffusion Monte Carlo simulations.