Nonlocal corrections to dynamical mean-field theory from the two-particle self-consistent method

Abstract

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.

arXiv comment15 pages, 19 figures. Changes from v2: added panels on some figures showing relative deviation from benchmarks, updated references. The self-energy results subsection has been slightly reworded

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• Spin correlations in the bilayer Hubbard model with perpendicular electric field
• Electron-magnon dynamics triggered by an ultrashort laser pulse: A real-time Dual $GW$ study
• Multi-orbital two-particle self-consistent approach -- strengths and limitations
• Dual-space cluster-diagrammatic approach to nonlocal electronic correlations