Semi-local observables from importance sampling diffusion Monte Carlo

An approach to evaluate a family of semi-local observables from the fixed-node ground state will be discussed. The celebrated importance-sampling diffusion Monte Carlo (DMC) method by Ceperley and Alder is a real space approach. Therefore, beyond the calculation of the total energy of the fixed-node ground state, DMC facilitates the evaluation of observables that are local in real space such as the density, albeit pure estimators or extrapolations are required. The evaluation of semi-local observables is expected to be more involved. It can be shown, however, that the DMC algorithm carries additional information of the fixed-node solution. DMC results for semi-local operators will be compared with exact results, in the hydrogen atom and the harmonic oscillator. The perspectives, computational cost, and potentials problems of this approach when applied to realistic many-body systems will be discussed.