Variational Monte Carlo for spin-orbit interacting systems

Recently, a diffusion Monte Carlo algorithm was applied to the study of spin-dependent interactions in condensed matter [A. Ambrosetti, F. Pederiva, E. Lipparini, and S. Gandolfi, Phys. Rev. B 80, 125306 ( 2009)]. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a general variational Monte Carlo approach is here introduced that treats in an efficient and very accurate way the spin degrees of freedom in atoms when spin-orbit effects are included in the Hamiltonian describing the electronic structure. We illustrate the algorithm on the evaluation of the spin-orbit splittings of isolated C, Tl, Pb, Bi, and Po atoms. In the case of the carbon atom, we investigate the differences between the inclusion of the spin orbit in its realistic and effective spherically symmetrized forms. The method exhibits a very good accuracy in describing the small energy splittings, opening the way for systematic quantum Monte Carlo studies of spin-orbit effects in atomic systems.