Benchmark of the TPSC+DMFT approach to the two-dimensional Hubbard Model

In quantum materials, 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 against published Diagrammatic Quantum Monte Carlo results [1,2] an approach that combines local observables from dynamical mean-field theory (DMFT) with the two-particle self-consistent theory (TPSC) [3]. This method (TPSC+DMFT) is relevant for weak to intermediate interactions and satisfies both the Mermin-Wagner theorem in two dimensions and the local Pauli principle. With this method, we find improvements for both spin and charge fluctuations and for the self-energy compared with TPSC. We also find that the accuracy check developed for TPSC is a good predictor of deviations from benchmarks. 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 with DMFT options.

[1] T. Schäfer et al., Phys. Rev. X 11, 011058 (2021).

[2] F. Šimkovic IV, R. Rossi, and M. Ferrero, ArXiv:2110.05863 [Cond-Mat] (2021).

[3] Y. M. Vilk and A.-M. S. Tremblay, J. Phys. I France 7, 1309 (1997).