Strong Electron Correlation in Materials from Pair-Interacting Model Hamiltonians

Abstract

Strong electron correlation in materials is explored within a class of model Hamiltonians that treat only pair interactions between electrons. The model is unique among typical spin Hamiltonians in that it does not have an effective mean-field reference wave function. The ground-state wave functions from all Hamiltonians in the model have the same one-electron reduced density matrix (1-RDM); consequently, one-electron theories such as the Hartree–Fock and density functional theories are inapplicable. In contrast, the ground-state two-electron reduced density matrix (2-RDM) has a one-to-one mapping to the ground-state wave function. For a range of lattices including linear, ladder, and square topologies, we variationally compute the 2-RDM subject to constraints, known as N-representability conditions, that are necessary for the 2-RDM to represent an N-electron ensemble density matrix. We find that for all model Hamiltonians the 2-RDM is accurately computed as long as the D, Q, and G N-representability cond...