Equation of state of two-dimensional He-3 at zero temperature

We have performed a quantum Monte Carlo study of a two-dimensional bulk sample of interacting 1/2-spin structureless fermions, a model of He-3 adsorbed on a variety of preplated graphite substrates. We have computed the equation of state and the polarization energy using both the standard fixed-node approximate technique with a simple backflow trial function and a formally exact methodology, relying on bosonic imaginary-time correlation functions of operators suitably chosen in order to extract fermionic energies. As the density increases, the fixed-node approximation predicts a transition to an itinerant ferromagnetic fluid, whereas the unbiased methodology indicates that the paramagnetic fluid is the stable phase until crystallization takes place. We find that two-dimensional He-3 at zero temperature crystallizes from the paramagnetic fluid at a density of 0.061 angstrom(-2) with a narrow coexistence region of 0.002 angstrom(-2). Remarkably, the spin susceptibility turns out in very good agreement with experiments.