Quadratic diffusion Monte Carlo algorithms for solving atomic many-body problems

The diffusion Monte Carlo algorithm with and without importance sampling is analyzed in terms of the algorithm’s underlying transfer matrix. The crucial role played by the Langevin algorithm in the importance-sampling process is made explicit and emphasized. The failure of existing second-order algorithms to converge quadratically for atomic many-body problems is shown to be caused by nonperturbative convergence errors due to the intrinsic inability of the Langevin algorithm to sample Slater orbitals. This failure can be simply circumvented by enforcing attractive cusp conditions on the trial function. Various new second-order diffusion Monte Carlo algorithms are systematically derived and their quadratic convergence numerically verified in cases of He and ${\mathrm{H}}_2$.