  We develop and test Quantum Monte Carlo algorithms which use a``twist'' or a
phase in the wave function for fermions in periodic boundary conditions. For
metallic systems, averaging over the twist results in faster convergence to the
thermodynamic limit than periodic boundary conditions for properties involving
the kinetic energy with the same computational complexity. We determine
exponents for the rate of convergence to the thermodynamic limit for the
components of the energy of coulomb systems. We show results with twist
averaged variational Monte Carlo on free particles, the Stoner model and the
electron gas using Hartree-Fock, Slater-Jastrow, three-body and backflow
wavefunction. We also discuss the use of twist averaging in the grand canonical
ensemble, and numerical methods to accomplish the twist averaging.
