Speaker
Description
We present exact large-scale Quantum Monte Carlo results for the one-dimensional Bose–Hubbard model with power-law hopping ∼ 1/r^α. For all 1 < α ≤ 3, we find that the superfluid–Mott-insulator transition at unit filling is continuous and scale invariant, and therefore incompatible with the Berezinskii–Kosterlitz–Thouless scenario recovered only for α > 3. We characterize this new universality class through finite-size scaling, data-collapse analysis, and a study of the excitation spectrum. Long-range hopping is also shown to qualitatively reshape the superfluid phase, yielding true long-range order for α ≤ 2 and an anomalous quasi-long-range-order regime for 2 < α ≤ 3. These results establish long-range hopping as a route to unconventional criticality in one-dimensional bosonic systems. We also briefly connect these ideas to collaborative numerical work on dipolar excitons in a lattice, where long-range hopping together with dipolar interactions supports excitonic supersolid behavior at fractional fillings.