Reduced density-matrix functionals applied to the Hubbard dimer

Abstract

Common density-matrix functionals, the Muller and the power functional, have been benchmarked for the half-filled Hubbard dimer, which allows us to model the bond dissociation problem and the transition from the weakly to the strongly correlated limit. Unbiased numerical calculations are combined with analytical results. Despite the well known successes of the Muller functional, the ground state is degenerate with a one-dimensional manifold of ferromagnetic solutions. The resulting infinite magnetic susceptibility indicates another qualitative flaw of the Muller functional. The derivative discontinuity with respect to particle number is not present indicating an incorrect metal-like behavior. The power functional actually favors the ferromagnetic state for weak interaction. Analogous to the Hartree-Fock approximation, the power functional undergoes a transition beyond a critical interaction strength, in this case, however, to a noncollinear antiferromagnetic state.