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.