Auxiliary Field Quantum Monte Carlo for systems with repulsive Coulomb interaction

In Chap. 1 some of the most popular QMC methods, Variational Monte Carlo (VMC), Green's Function Monte Carlo (GFMC) and Diffusion Monte Carlo (DMC) are reviewed. Then the HST formalism is presented in general terms, with the introduction of auxiliary fields, and some arguments are put forward about the potential advantages of the AFQMC method in comparison with other stochastic approaches. In Chap. 2 this technique is specifically developed in a way suitable for our particular problem with a Coulomb electron-electron interaction. Chap. 3 contains a brief discussion about the technicalities of our practical algorithm and about the methods one can adopt to perform the functional integral by efficiently sampling the auxiliary fields. In Chap. 4 the serious fluctuation problem is illustrated, the basic causes which give rise to this difficulty are discussed and a possible solution to the problem, i.e. a different formulation of the AFQMC technique, is introduced, together with some technical improvements we have developed in order to make the method really efficient and practically applicable. In Chap. 5 we give a concise but exhaustive description of many numerical tests performed to check the reliability of our algorithm, by comparing AFQMC simulations results for the H2 molecule with exact (full Cl) corresponding data. Finally, our calculations of several physical properties of H2 and H3 are presented.