Quantum phase transitions of interacting bosons on hyperbolic lattices

Understand

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 Schl\"afli 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.