Elementary Building Blocks for Cluster Mott Insulators

Mott insulators, in which strong Coulomb interactions fully localize electrons on single atomic sites, play host to an incredibly rich and exciting array of strongly correlated physics. One can naturally extend this concept to cluster Mott insulators, wherein electrons localize not on single atoms but across clusters of atoms, forming ``molecules in solids''. The resulting localized degrees of freedom incorporate the full spectrum of electronic degrees of freedom, spin, orbital, and charge. These serve as the building blocks for cluster Mott insulators, and understanding them is an important first step toward understanding the many-body physics that emerges in candidate cluster Mott insulators. Here, we focus on elementary building blocks, neglecting some of the complexity present in real materials which can often obfuscate the underlying principles at play. Through an extensive set of exact theoretical calculations on clusters of varying geometry, number of orbitals, and number of electrons, we uncover some of the basic organizing principles of cluster Mott phases, particularly when interactions dominate and negate a simple single-particle picture. These include, for example, the identification of an additional ``cluster Hund's rule'', of cluster ground states that are best understood from a purely interacting perspective, and of several localized degrees of freedom which are protected by an unusual combination of discrete spatial or orbital symmetries. Finally, we discuss the impact of adding additional terms, relevant to material candidates, on the phase diagrams presented throughout, as well as the potential next steps in the journey to building a more complete picture of cluster Mott insulators.