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The Bose--Hubbard Model and Superfluid Staircases in $^{4}$He Films

G. T. Zimanyi·P. A. Crowell·R. T. Scalettar·G. G. Batrouni
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Abstract

The recent experimental observation of step-like structure in the superfluid density of $^{4}$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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G. T. Zimanyi, P. A. Crowell, R. T. Scalettar, G. G. Batrouni. 1993-10-26. The Bose--Hubbard Model and Superfluid Staircases in $^{4}$He Films. https://doi.org/10.1103/physrevb.50.6515

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