Certain exact many-body results for Hubbard model ground states testable in small quantum dot arrays

We present several interesting phenomena related to flat-band ferromagnetism in the Hubbard model. The first is a mathematical theorem stating certain conditions under which a flat-band ferromagnetic must necessarily be degenerate with a nonferromagnetic state. This theorem is generally applicable and geometry independent but holds only for a small number of holes in an otherwise filled band. The second phenomenon is a peculiar example where the intuition fails that particles prefer to doubly occupy low-energy states before filling higher-energy states. Lastly, we show a pattern of ferromagnetism which appears in small pentagonal and hexagonal plaquettes at filling factors of roughly 3/10 and 1/4. These examples require only a small number of lattice sites and may be observable in quantum dot arrays currently available as laboratory spin qubit arrays.

Automated summary

We discuss interesting phenomena in the Hubbard model related to flat-band ferromagnetism. The first is a mathematical theorem that describes the conditions for degeneracy between a flat-band ferromagnetic and a nonferromagnetic state. This theorem is generally applicable and independent of geometry, but only holds for a small number of holes in a filled band. The second phenomenon challenges intuition by showing an example where particles do not prefer to doubly occupy low-energy states before filling higher-energy states. Lastly, we present a pattern of ferromagnetism in small pentagonal and hexagonal plaquettes at specific filling factors. These examples can be observed in quantum dot arrays available in laboratories.