Dynamical structure functions from quantum Monte Carlo calculations of a proper integral transform

Abstract

An ab initio method for determining the dynamical structure function of an interacting many-body quantum system has been devised by combining a generalized integral transform method with quantum Monte Carlo (QMC) methods. A kernel has been found that (i) lets the transform be calculable with QMC methods and (ii) is a representation of the $\ensuremath{\delta}$ function, allowing an inversion of the transform with a much higher predictive power than the inverse Laplace transform. As a first application, the excitation spectrum of bulk atomic ${}^{4}$He has been computed, both in the low and intermediate momentum ranges. The peculiar form of the kernel allows us to predict, without using any model, both positions and widths of the collective excitations in the maxon-roton region, as well as the existence of the second collective peak. A prediction of the dispersion of the single-particle modes described by the incoherent part is also presented.