Reduced density-matrix functionals applied to the Hubbard dimer

TL;DR

This paper benchmarks common density-matrix functionals, like Müller and power functionals, on the Hubbard dimer, revealing their strengths and flaws in modeling correlation effects and magnetic properties.

Contribution

It provides a comparative analysis of Müller and power functionals on the Hubbard dimer, highlighting their qualitative and quantitative limitations.

Findings

Müller functional's ground state is degenerate with ferromagnetic solutions.

Müller functional shows infinite magnetic susceptibility, indicating a flaw.

Power functional favors ferromagnetic state at weak interactions and transitions to antiferromagnetic beyond a critical point.

Abstract

Common density-matrix functionals, the M\"uller 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 M\"uller functional, the ground state is degenerate with a one-dimensional manifold of ferromagnetic solutions. The resulting infinite magnetic susceptibility indicates another qualitative flaw of M\"uller's 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 non-collinear antiferromagnetic state.