Norm-conserving diffusion Monte Carlo method and diagrammatic expansion of interacting Drude oscillators: Application to solid xenon

Abstract

The quantum Drude oscillator (QDO) model, which allows many-body polarization and dispersion to be treated both on an equal footing and beyond the dipole limit, is investigated using two approaches to the linear scaling diffusion Monte Carlo (DMC) technique. The first is a general purpose norm-conserving DMC (NC-DMC) method wherein the number of walkers, $N$, remains strictly constant thereby avoiding the sudden death or explosive growth of walker populations with an error that vanishes as $\mathcal{O}({N}^{\ensuremath{-}1})$ in the absence of weights. As NC-DMC satisfies detailed balance, a phase space can be defined that permits both an exact trajectory weighting and a fast mean-field trajectory weighting technique to be constructed which can eliminate or reduce the population bias, respectively. The second is a many-body diagrammatic expansion for trial wave functions in systems dominated by strong on-site harmonic coupling and a dense matrix of bilinear coupling constants such as the QDO in the dipole limit; an approximate trial function is introduced to treat two-body interactions outside the dipole limit. Using these approaches, high accuracy is achieved in studies of the fcc-solid phase of the highly polarizable atom, xenon, within the QDO model. It is found that 200 walkers suffice to generate converged results for systems as large as 500 atoms. The quality of QDO predictions compared to experiment and the ability to generate these predictions efficiently demonstrate the feasibility of employing the QDO approach to model long-range forces.