The variational and diagrammatic quantum Monte Carlo approach to the many-electron problem*

Two of the most influential ideas developed by Richard Feynman are the Feynman diagram technique and his variational approach. Here we show that combining both, and introducing a diagrammatic quantum Monte Carlo method, results in a powerful and accurate solver to the generic solid state problem, in which a macroscopic number of electrons interact by the long-range Coulomb repulsion. We apply it to the quintessential problem of solid state, the uniform electron gas, which is at the heart of the density functional theory success in describing real materials, yet it has not been adequately solved for over 90 years. Our method allows us to calculate numerically exact momentum and frequency resolved spin and charge response functions. This method can be applied to a number of moderately interacting electron systems, including models of realistic metallic and semiconducting solids.