| Summary: | The energy of ultra-dilute quantum many-body systems is known to exhibit a
universal dependence on the gas parameter $x=n a_0^d$, with $n$ the density,
$d$ the dimensionality of the space ($d=1,2,3$) and $a_0$ the $s$-wave
scattering length. The universal regime typically extends up to $x\approx
0.001$, while at larger values specific details of the interaction start to be
relevant and different model potentials lead to different results. Dipolar
systems are peculiar in this regard since the anisotropy of the interaction
makes $a_0$ depend on the polarization angle $\alpha$, so different
combinations of $n$ and $\alpha$ can lead to the same value of the gas
parameter $x$. In this work we analyze the scaling properties of dipolar bosons
in two dimensions as a function of the density and polarization dependent
scattering length up to very large values of the gas parameter $x$. Using
Quantum Monte Carlo (QMC) methods we study the energy and the main structural
and coherence properties of the ground state of a gas of dipolar bosons by
varying the density and scattering length for fixed gas parameter. We find that
the dipolar interaction shows relevant scaling laws up to unusually large
values of $x$ that hold almost to the boundaries in the phase diagram where a
transition to a stripe phase takes place.
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