Bose-Hubbard model and superfluid staircases in 4He films.

The recent experimental observation of steplike structure in the superfluid density of $^{4}\mathrm{He}$ films on graphite is interpreted in terms of passage close to Mott insulating lobes in the Bose-Hubbard model. Plateaus develop in the superfluid density near the completion of each layer because of the He-He repulsion. We modify the Bose-Hubbard Hamiltonian, using a density-dependent He-He interaction term to model the He-substrate potential. Quantum Monte Carlo simulations yield results that agree well with the experimental data.