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modulus for instance, and it could simply be an artifact of our approximation, but let us take it as a hypothesis. Whereas a Wigner crystal phase occurs at low density in three dimensions, it occurs at high density in two dimensions[33]. The possibility of crystal phases for repulsive bosons was studied in [9]. For Coulomb repulsion with strength e $^{2}$, the thermodynamic state of a classical Coulomb system is determined by Γ = √$_{πn e}$ $^{2}$/k$_{B}$ T , where n is the density. Experimentally it was found that Γ ≈ 137[34], which gives a critical density 

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On the other hand, since our model has point-like interactions, and is in the unitary limit, the conditions for a crystal phase are expected to be different. In particular our formula eq. (95) has no e 2 dependence, and this leads to a linear in T dependence. 

