Extraction of the frequency moments of spectral densities from imaginary-time correlation function data

We introduce an exact framework to compute the positive frequency moments M^ () (q) =^ of different dynamic properties from imaginary-time quantum Monte Carlo data. As a practical example, we obtain the first five moments of the dynamic structure factor S (q, ) of the uniform electron gas at the electronic Fermi temperature based on ab initio path integral Monte Carlo simulations. We find excellent agreement with known sum rules for =1, 3, and present results for =2, 4, 5. Our idea can be straightforwardly generalized to other dynamic properties such as the single-particle spectral function A (q, ), and will be useful for a number of applications, including the study of ultracold atoms, exotic warm dense matter, and condensed matter systems.