Two-particle self-consistent approach combined with dynamical mean field theory: A real-frequency study of the square-lattice Hubbard model

We investigate the two-dimensional Hubbard model using a real-frequency implementation of the $\mathrm{TPSC}+\mathrm{DMFT}$ approach. This hybrid method combines the nonlocal correlations captured by the two-particle self-consistent (TPSC) approach with the local dynamical correlations of dynamical mean field theory (DMFT). The results demonstrate that $\mathrm{TPSC}+\mathrm{DMFT}$ effectively describes pseudogap physics and nonlocal fluctuations in the moderately correlated regime, while also reproducing the Mott insulating state at larger interaction strengths. For doped Mott insulators, we find that $\mathrm{TPSC}+\mathrm{DMFT}$ captures the evolution of Fermi pockets into Fermi arcs, consistent with the results from cluster DMFT and photoemission studies. These findings highlight the capability of $\mathrm{TPSC}+\mathrm{DMFT}$ to bridge the gap between weak and strong coupling physics in Hubbard models, providing insights into spin and charge fluctuations, as well as their role in the pseudogap formation.