Hellmann and Feynman theorem versus diffusion Monte Carlo experiment

In a computer experiment the choice of suitable estimators to measure a physical quantity plays an important role. We propose a new direct route to determine estimators for observables which do not commute with the Hamiltonian. Our new route makes use of the Hellmann and Feynman theorem and in a diffusion Monte Carlo simulation it introduces a new bias to the measure due to the choice of the auxiliary function. This bias is independent from the usual one due to the choice of the trial wave function. We used our route to measure the radial distribution function of a spin one half Fermion fluid.

► Importance of the choice of suitable estimators to measure a physical quantity in MC. ► Hellmann and Feynman theorem as a route to determine estimators for observables. ► Our beta correction of Eq. (5) for a diffusion MC calculation is new in the literature. ► In a diffusion Monte Carlo simulation the HF theorem introduces a new bias to the measure. ► Explicit example for the calculation of the g(r) of a specific Fermion fluid.