Quantum phase transitions of interacting bosons on hyperbolic lattices

The effect of many-body interaction in curved space is studied based on the extended Bose--Hubbard model hyperbolic lattices. Using mean-field approximation and quantum Monte Carlo simulation, phase diagram explicitly mapped out, which contains superfluid, supersolid insulator phases at various fillings. Particularly, it revealed that sizes Mott lobes shrink stabilized smaller nearest-neighbor as $q$ Schl\"afli symbol increases. underlying physical mechanism attributed to increase coordination number, hence kinetic energy interaction. results suggest lattices may be a unique platform study number transitions, relevant experiments ultracold atoms optical