摘要
Model Hamiltonians are regularly derived from first principles to describe correlated matter.However,the standard methods for this contain a number of largely unexplored approximations.For a strongly correlated impurity model system,here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited-state energies and wave functions using state-of-the-art first-principles many-body wave function approaches.To this end,we use the vanadocene molecule and analyze all downfolding aspects,including the Hamiltonian form,target basis,double-counting correction,and Coulomb interaction screening models.Wefind that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results,while orbital-dependent double-counting corrections diminish the quality.Background screening of the Coulomb interaction matrix elements primarily affects crystal-field excitations.Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.
基金
supported by the U.S
E.v.L.acknowledges support from the Swedish Research Council(Vetenskapsrådet,VR)under grant 2022-03090
C.E.D.acknowledges support from NSF Grant No.DMR-2237674
The Flatiron Institute is a division of the Simons Foundation
T.W.acknowledges support from the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)through the cluster of excellence“CUI:Advanced Imaging of Matter”of the Deutsche Forschungsgemeinschaft(DFG EXC 2056,Project ID 390715994)
research unit QUAST FOR 5249(project ID:449872909,project P5)
supported by a grant from the Simons Foundation as part of the Simons Collaboration on the many-electron problem
M.R.thanks the Flatiron Institute for hospitality and acknowledges financial support from the Dutch research program‘Materials for the Quantum Age’(QuMat).
