FINITE-SIZE EFFECTS AND COULOMB INTERACTIONS IN QUANTUM MONTE-CARLO CALCULATIONS FOR HOMOGENEOUS SYSTEMS WITH PERIODIC BOUNDARY-CONDITIONS

Quantum Monte Carlo (QMC) calculations are only possible in finite sys tems and so solids and liquids must be modeled using small simulation cells subject to periodic boundary conditions. The resulting finite-si ze errors are often corrected using data from local-density functional or Hartree-Fock calculations, but systematic errors remain after thes e corrections have been applied, The results of our jellium QMC calcul ations for simulation cells containing more than 600 electrons confirm that the residual errors are significant and decay very slowly as the system size increases. We show that they are sensitive to the form of the model Coulomb interaction used in the simulation cell Hamiltonian and that the usual choice, exemplified by the Ewald summation techniq ue, is not the best. The finite-size errors can be greatly reduced and the speed of the calculations increased by a factor of 20 if a better choice is made. Finite-size effects plague most methods used for exte nded Coulomb systems and many of the ideas in this paper are quite gen eral: they may be applied to any type of quantum or classical Monte Ca rlo simulation, to other many-body approaches such as the GW method, a nd to Hartree-Fock and density-functional calculations.