Reduced density-matrix functionals applied to the Hubbard dimer

Abstract

Common density-matrix functionals, the Müller and the power functional, have been benchmarked for the half-filled Hubbard dimer, which allows 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 Müller 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 Müller functional. The derivative discontinuity with respect to particle number is not present indicating an incorrect metallike 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 non-collinear antiferromagnetic state.

Reduced density-matrix functionals from many-particle theory

“…We have however shown that the Müller functional predicts an unphysical infinite magnetic susceptibility for the half-filled Hubbard dimer [19]. It is also known to overcorrelate [55][56][57].…”

“…Due to the construction of the power functional by interpolation it inherits several problems from the limits [19]: We have shown that on the one hand it is missing the derivative discontinuity of the energy at integer particle numbers like the Müller functional and that it on the other hand yields an unphysical transition to an antiferromagnetic state like the Hartree-Fock approximation. The power functionals also shows a plethora of unphysical non-collinear magnetic structures and transitions.…”

“…The deficiencies of explicit RDMFs [19] discussed earlier suggest to explore implicit functionals. Implicit functionals provide a solid basis for including static correlation effects and they hold promise to provide new ideas for the development of new explicit functionals.…”

“…The simplest mapping from a 1-RDM to a Green's function, that reproduces the 1-RDM, is given by equation (19). This simple mapping however leads to the breakdown of the perturbation expansion at low temperatures [126].…”

“…We describe the DFT+RDMFT scheme and new approaches to approximate the density-matrix functional. New functionals are necessary, because despite the success of simple functionals within RDMFT, the most common density-matrix functionals reproduce a number of features in a qualitatively incorrect manner [17][18][19]]. …”