  We implement the phaseless auxiliary field quantum Monte Carlo method using
the plane-wave based projector augmented wave method and explore the accuracy
and the feasibility of applying our implementation to solids. We use a singular
value decomposition to compress the two-body Hamiltonian and thus reduce the
computational cost. Consistent correlation energies from the primitive-cell
sampling and the corresponding supercell calculations numerically verify our
implementation. We calculate the equation of state for diamond and the
correlation energies for a range of prototypical solid materials. A
down-sampling technique along with natural orbitals accelerates the convergence
with respect to the number of orbitals and crystal momentum points. We
illustrate the competitiveness of our implementation in accuracy and
computational cost for dense crystal momentum point meshes comparing to a
well-established quantum-chemistry approach, the coupled-cluster ansatz
including singles, doubles and perturbative triple particle-hole excitation
operators.
