  Theoretical methods that are accurate for both short-distance observables and
long-wavelength collective modes are still being developed for the Hubbard
model. Here, we benchmark an approach that combines dynamical mean-field theory
(DMFT) observables with the two-particle self-consistent theory (TPSC). This
offers a way to include non-local correlations in DMFT while also improving
TPSC. The benchmarks are published diagrammatic quantum Monte Carlo results for
the two-dimensional square lattice Hubbard model with nearest-neighbor hopping.
This method (TPSC+DMFT) is relevant for weak to intermediate interaction,
satisfies the local Pauli principle and allows us to compute a spin
susceptibility that satisfies the Mermin-Wagner theorem. The DMFT double
occupancy determines the spin and charge vertices through local spin and charge
sum rules. The TPSC self-energy is also improved by replacing its local part
with the local DMFT self-energy. With this method, we find improvements for
both spin and charge fluctuations and for the self-energy. We also find that
the accuracy check developed for TPSC is a good predictor of deviations from
benchmarks for this model. TPSC+DMFT can be used in regimes where quantum Monte
Carlo is inaccessible. In addition, this method paves the way to multi-band
generalizations of TPSC that could be used in advanced electronic structure
codes that include DMFT.
