single band Hubbard model (HM), is known, for example, to be insulating and to exhibit long range antiferromagnetic (AF) order at half-filling on a square lattice [@hirsch85; @hirsch89] for any ratio of the on-site interaction $U$ to hopping $t$, and to undergo a paramagnetic metal to insulating AF transition above a nonzero critical $U_c$ on other geometries such as the honeycomb lattice. The Nagaoka theorem[@nagaoka66] notwithstanding, the ferromagnetic behavior which is robust within mean-field theory[@fazekas99; @hirsch85], seems to be difficult to achieve when the single band Hamiltonian is solved with more exact methods[@tasaki98].

The generalization of tight-binding Hamiltonians to multiple bands opens up a richer variety of magnetic behavior. In the case of the periodic Anderson model (PAM), the interplay of the on-site repulsion $U_f$ on localized ($f$) orbitals with the hybridization $V$ to a noninteracting conduction ($d$) band results in a competition of long range magnetic order arising from the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction (at small $V$) and spin liquid behavior (at large $V$).[@Vekic95; @stewart01; @DeLeo08; @Hu17] Not uncommonly in these more complex situations, orbital ordering coexists with spin ordering[@cameron16].

Many of these models offer quite remarkable insights into strongly correlated materials; for instance, the HM replicates several prominent qualitative 