Effective Mass Puzzle in the Electron Gas in Two and Three Dimensions*

We have developed a new systematic quantum field theory approach to investigate the effective mass of the uniform electron gas in the density regime applicable to simple metals. Using diagrammatic Monte Carlo based on the computational graph representation and Taylor-mode automatic differentiation, we are able to calculate the effective mass up to high orders in perturbation theory, finding that we achieve good convergence thanks to the cancellation of vertex corrections. We show numerical evidence that the quasiparticle effective mass is nearly identical to the bare electron mass despite strong renormalization from the Coulomb repulsion in both two and three dimensions and reaffirm that the effective mass renormalization owes primarily to charge fluctuations in the metallic regime.