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 ( α ) ( q ) = (cid:104) ω α (cid:105) 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 , ω ) 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 α = 1 , 3, and, to our knowledge, present the first results for α = 2 , 4 , 5. Our idea can be straightforwardly generalized to other dynamic properties such as the single-particle spectral function A ( q , ω ), and will be useful for a number of applications, including the study of ultracold atoms, exotic warm dense matter, and condensed matter systems.

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