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We present a technique that enables the evaluation of perturbative expansionsbased on one-loop-renormalized vertices up to large expansion orders.Specifically, we show how to compute large-order corrections to the randomphase approximation in either the particle-hole or particle-particle channels.The algorithm's efficiency is achieved by the summation over contributions ofall symmetrized Feynman diagram topologies using determinants, and byintegrating out analytically the two-body long-range interactions in order toyield an effective zero-range interaction. Notably, the exponential scaling ofthe algorithm as a function of perturbation order leads to a polynomial scalingof the approximation error with computational time for a convergent series. Toassess the performance of our approach, we apply it to the non-perturbativeregime of the square-lattice fermionic Hubbard model away from half-filling andreport, as compared to the bare interaction expansion algorithm, significantimprovements of the Monte Carlo variance as well as the convergence propertiesof the resulting perturbative series.

Efficient One-Loop-Renormalized Vertex Expansions with Connected Determinant Diagrammatic Monte Carlo