Equation of state of two--dimensional ${}^3$He at zero temperature

Abstract

We have performed a Quantum Monte Carlo study of a two-dimensional bulk sample of interacting 1/2-spin structureless fermions, a model of ${}^3$He 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 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 ${}^3$He at zero temperature crystallizes from the paramagnetic fluid at a density of 0.061 Å${}^{-2}$ with a narrow coexistence region of about 0.002 Å${}^{-2}$. Remarkably, the spin susceptibility turns out in very good agreement with experiments.

7 pages, 7 figures

References in corpus (3)

• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Exact ground state Monte Carlo method for Bosons without importance sampling
• The itinerant ferromagnetic phase of the Hubbard model

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