Ferromagnetism in the quantum-dot-based Hubbard model

The Hubbard model, though vastly important throughout many areas of condensed matter physics, is unsolved in the general case. Due to their exponential complexity, classical simulations of the Hubbard model struggle for more than a few tens of lattice sites, suggesting that quantum simulations may be necessary to fully understand these systems. In fact, such simulations are already being performed on quantum dot devices, prompting the question, what interesting condensed matter effects can be observed in systems of less than 10 quantum dots? One notable effect is the existence of nontrivial magnetic phases. Spins in Hubbard model systems generally prefer to be anti-aligned; however, in certain cases when a band is close to, but not exactly half-filled, the model can prefer a ferromagnetic, or partially ferromagnetic ground state. The most well-known example of this effect is Nagaoka ferromagnetism, but nontrivial ferromagnetism can occur in other systems which are not directly explained by Nagaoka's theorem. This talk presents an overview of several ground-state ferromagnetic effects exhibited in systems of just a few lattice sites, including ferromagnetism in pentagon and hexagon plaquettes at filling factors of 3/10 and 1/4 respectively, as well as ferromagnetism in bilayer systems. Due to the small number of dots needed, these effects can potentially be observed in experimental devices currently, or in the near future.