Extended Hubbard Model realized in 2D clusters of molecular anions

Abstract: The Hubbard model, despite its simplicity, is remarkably successful at describing numerous many-body phenomena. However, due to the small class of problems which can be solved exactly, there has been substantial interest in quantum simulations of extended Hubbard models to in turn, simulate materials and the interaction-driven phases they host. Here, we study small clusters of molecular anions of 3,4,9,10-perylene tetracarboxylic dianhydride on NaCl bilayers on Ag(111) using non-contact Atomic Force Microscopy, Electrostatic Force Spectroscopy, and Scanning Tunnelling Microscopy and Spectroscopy, and show that the occupation and transition energies are well described by an extended Hubbard model. In particular, asymmetric clusters of four molecules require the addition of differing inter-site electrostatic interaction terms and on-site potentials, as well as asymmetric hoping terms. With $t<<U$, occupation asymmetry is driven by these terms, independent of U. The good agreement between the model and the data indicate such molecular anion clusters could be used to probe larger systems and a more varied phase space of realistic fermionic Hubbard models.