As has been shown in earlier chapters, many-body simulation techniques
such as the variational and diffusion Quantum Monte Carlo (QMC)
methods are capable of yielding highly accurate results for correlated
systems. In chapter 
the technique of modelling
large systems using a finite simulation cell subject to periodic
boundary conditions was introduced. The use of a finite cell
introduces ``finite size effects'' which are often very important,
particularly for systems with long ranged interactions such as the
Coulomb interaction. In this chapter a method is introduced for
dealing with long ranged interactions in quantum many-body simulations
which greatly reduces these finite size effects.
The finite size effects encountered in QMC calculations for electronic
systems can be divided into two terms: (i) the independent particle
finite size effect (IPFSE)[33, 50], and (ii) the
Coulomb finite size effect (CFSE) [3, 46].
The IPFSE and CFSE are most easily defined with reference to results
of local density approximation (LDA) calculations. The IPFSE is the
difference between the LDA energies per atom in the finite and
infinite systems and the CFSE is the remainder of the finite size
error. Recently a method was introduced
[33, 50] for reducing the IPFSE in insulating
systems by using the ``special k-points'' method borrowed from
bandstructure theory [70, 54]. This has already been
described in detail in chapter ,
section . This method reduces the IPFSE by an order of
magnitude in insulators and leaves the CFSE as the dominant finite
size effect. The CFSE, which is the subject of this chapter, arises
from the long range of the Coulomb interaction and is therefore of
wide significance in many-body simulations.