Semideterministic and stochastic sampling of Feynman diagrams with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:mrow><mml:mi>f</mml:mi></mml:msub></mml:math>

We introduce a family of (semi)-bold-line series, assisted with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>1</a:mn><a:mo>/</a:mo><a:msub><a:mi>N</a:mi><a:mi>f</a:mi></a:msub></a:mrow></a:math> expansions, with <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>N</b:mi><b:mi>f</b:mi></b:msub></b:math> being the number of fermion flavors. If there is no additional <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>N</c:mi><c:mi>f</c:mi></c:msub></c:math> cut, the series reduces to the random phase approximation series in the density-density channel, complementary to the particle-hole and particle-particle channels introduced in . To address the very localized integrands in diagrammatic Monte Carlo, we introduced an innovative VEGAS-RG-MCMC sampling method, where we found a significant decrease of autocorrelation time without the usage of the state-of-the-art many-configuration MCMC (MCMCMC) method while the combination of both is also straightforward. We performed extensive benchmarks for density, energy, and pressure with the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>t</d:mi><d:mtext>−</d:mtext><d:msup><d:mrow><d:mi>t</d:mi></d:mrow><d:mo>′</d:mo></d:msup></d:mrow><d:mo> </d:mo><d:mrow><d:mi>SU</d:mi><d:mo>(</d:mo><d:msub><d:mi>N</d:mi><d:mi>f</d:mi></d:msub><d:mo>)</d:mo></d:mrow></d:math> Hubbard model on a square lattice and honeycomb lattices over a wide range of numerical methods. For benchmark purposes, we also implement bare-<e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi mathvariant="normal">U</e:mi></e:math> symmetry-broken perturbation series for the two-dimensional SU(2) Hubbard model on the honeycomb lattice, where we found encouraging results from weak to intermediate couplings.