Zero-temperature equation of state of two-dimensional 3He

The equation of state of two-dimensional $^3$He at zero temperature has been calculated using the diffusion Monte Carlo method. By means of a combination of the fixed-node and released-node techniques it is shown that backflow correlations provide a very accurate equation of state. The results prove unambiguously the non-self-bound character of two-dimensional $^3$He due to its Fermi statistics. We present solid evidence that the gas phase, predicted for the two-dimensional system, can be extrapolated to the case of $^3$He adsorbed on a strong substrate like graphite.