Elementary Building Blocks for Cluster Mott Insulators

The Hubbard model provides a rich playground for investigating the physics of a wide range of strongly correlated systems. An important limit in the model is the Mott insulating regime, where, at half-filling, electrons are localized on single atomic sites. In this work, we investigate extensions of this idea to cluster Mott insulators-- where electrons are now localized on clusters of sites. To that end, we study a plethora of different clusters, at different integer fillings, by constructing a general Hamiltonian for each cluster. This allows us to explore different regimes of the interplay of strong correlations and hopping within these clusters, and their respective emergent effective degrees of freedom. We then go beyond the single-orbital "cluster" Hubbard model and include multiple orbitals and interactions between them, including spin-orbit coupling. With these building blocks established, it will be possible to introduce inter-cluster hopping terms into the picture; depending on the nature of the resulting effective interactions, they can give rise to novel Hamiltonians, which might possibly host highly correlated and/or frustrated phases.