Mean-field approximation of the Fermi–Hubbard model expressed in a many-body basis

The effective independent-particle (mean-field) approximation of the Fermi–Hubbard Hamiltonian is described in a many-body basis to develop formal comparison with exact diagonalization full model using small atomic chain as test systems. This allows for development an intuitive understanding shortcomings mean-field and how critical correlation effects are missed this popular approach. description highlights potential ambiguity related definition density states. Specifically, satellite peaks shown emerge approximation, departure from common belief that they characterize effects. scheme emphasizes importance different corrections can improve description. pedagogical treatment expected make it possible researchers acquire improved found various areas electronic properties molecules solids.