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

Automated summary

By utilizing the extended Bose-Hubbard model on hyperbolic lattices, the study examines the impact of many-body interactions, revealing that the Mott lobes decrease in size as q in the Schlafli symbol increases, and the supersolid is stabilized under smaller nearest-neighbor interactions. This phenomenon is attributed to the increase in coordination number, leading to higher kinetic energy and nearest-neighbor interaction. The results propose that hyperbolic lattices could serve as a unique platform for investigating the influence of coordination numbers on quantum phase transitions, which may have implications for experiments involving ultracold atoms in optical lattices.