Bose-Hubbard model on polyhedral graphs

Ever since the first observation of Bose-Einstein condensation in 1990s, ultracold quantum gases have been subject intense research, providing a unique tool to understand behavior matter governed by laws mechanics. Ultracold bosonic atoms loaded an optical lattice are usually described Bose-Hubbard model or variant it. In addition common insulating and superfluid phases, other phases (such as density waves supersolids) may show up presence short-range interparticle repulsion also depending on geometry lattice. We herein explore this possibility, using graph convex polyhedron ``lattice'' playing with coordination nodes promote wanted finite-size ordering. To accomplish job we employ decoupling approximation, whose efficacy is tested one case against exact diagonalization. report zero-temperature results for two Catalan solids, tetrakis hexahedron pentakis dodecahedron, which thorough ground-state analysis reveals existence ``phases'' polyhedral order widely extended supersolid region. The key outcome unbalance between inequivalent graph. predicted can be probed systems programmable holographic tweezers.