Abstract
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.
Highlights
Two of the most influential ideas developed by Richard Feynman are the Feynman diagram technique and his variational approach
The resulting Variational Diagramatic Monte Carlo (VDMC) method is a generic manybody solver, which is here tested on the classic solid state problem
The effect of the interaction is included with a power expansion in ΔL, constructed using the Feynman diagrams
Summary
Two of the most influential ideas developed by Richard Feynman are the Feynman diagram technique and his variational approach. 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. 1234567890():,; The success of the Feynman’s diagram technique[1] rests on two pillars, the quality of the chosen starting point and one’s ability to compute the contributions of high-enough order, so that the sum can be extrapolated to the infinite order We address the former by introducing the variationally optimized starting point, as discussed below, and we solve the latter by developing a powerful Monte Carlo method which can sum factorially large number of diagrams while massively reducing the fermionic sign problem by organizing Feynman diagrams into sign-blessed groups. The accuracy of the calculated response functions is sufficiently high, so as to uncover previously missed fine structure in these responses
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