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.

In the accompanying paper (see link), we presented illustrative phase diagrams for different cluster geometries and select electron fillings. Here, we present the raw data and phase diagrams for all the remaining electron fillings on all cluster geometries obtained from exact diagonalization. The data is presented in Arrow files, with each Arrow file containing data such as eigenvalues, eigenvectors, ground state degeneracies, and various quantum numbers for a 21x21 U-J grid for all electron fillings, with the specific hopping values specified in the file name. The plots in the dataset have been derived from the respective raw data files.