Sign Blessing in the Diagrammatic Space of the Jellium Model

The jellium model is a basic model of fundamental importance. Quantitative knowledge of its thermodynamics, quasiparticle excitations, and dielectric responses is the starting point for properly treating the Coulomb interaction in more realistic systems. However, numerous numerical methods can either offer only partial information or rely on approximations with unknown systematic bias. Monte Carlo sampling of Feynman diagrams to high-order is a generic way to solve this problem but the best strategy for simulating the diagrammatic space of skeleton diagrams remains unknown. Given that sign-alternating Feynman diagrams for fermions are known to cancel each other, it is crucially important to better understand the precise mechanisms behind this sign-blessing phenomenon that leads to better series behavior. We explore relative merits of various approaches based on different representations (real space vs momentum space and imaginary time vs Matsubara frequencies), explicit variables symmetrization, and explicit summation over all, or selected sub-classes, of diagram topologies.