The Bose--Hubbard Model and Superfluid Staircases in $^{4}$He Films
G.T. Zimanyi, P.A. Crowell, R.T. Scalettar, and G.G. Batrouni
TL;DR
This paper explains the step-like superfluid density in helium-4 films on graphite using a modified Bose--Hubbard model with density-dependent interactions, supported by quantum Monte Carlo simulations matching experimental observations.
Contribution
It introduces a density-dependent He-He interaction in the Bose--Hubbard model to accurately reproduce superfluid staircases in helium films.
Findings
Quantum Monte Carlo results align with experimental data.
Plateaus in superfluid density correspond to Mott insulating lobes.
Modified model captures layer completion effects.
Abstract
The recent experimental observation of step-like structure in the superfluid density of 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 which agree well with the experimental data.
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