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

Automated summary

We propose an accurate framework for computing positive frequency moments M(alpha)(q) = (omega alpha) of different dynamic properties from imaginary-time quantum Monte Carlo data. As an application, we calculate the first five moments of the dynamic structure factor S(q, omega) of the uniform electron gas at the electronic Fermi temperature using ab initio path integral Monte Carlo simulations. We demonstrate excellent agreement with known sum rules for alpha = 1, 3, and provide results for alpha = 2, 4, 5. Our approach can be extended to other dynamic properties such as the single-particle spectral function A(q, omega), and has wide-ranging applications in studying ultracold atoms, exotic warm dense matter, and condensed matter systems.