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The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter x=n a_0^dx=na0d, with nn the density, dd the dimensionality of the space (d=1,2,3d=1,2,3) and a_0a0 the ss-wave scattering length. The universal regime typically extends up to x\approx 0.001x≈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_0a0 depend on the polarization angle \alphaα, so different combinations of n and \alphaα 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 gas parameter values. 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 a fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of xx that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.

We study the repulsive Fermi polaron in a two-component, two-dimensional system of fermionic atoms inspired by the results of a recent experiment with 173Yb atoms [N. Darkwah Oppong et al., Phys. Rev. Lett. 122, 193604 (2019)]. We use the diffusion Monte Carlo method to report properties such as the polaron energy and the quasiparticle residue that have been measured in that experiment. To provide insight into the quasiparticle character of the problem, we also report results for the effective mass. We show that the effective range, together with the scattering length, is needed in order to reproduce the experimental results. Using different model potentials for the interaction between the Fermi sea and the impurity, we show that it is possible to establish a regime of universality, in terms of these two parameters, that includes the whole experimental regime. This illustrates the relevance of quantum fluctuations and beyond mean-field effects to correctly describe the Fermi polaron problem., This work has been partly supported by the MINECO (Spain) Grant No. FIS2017-84114-C2-1-P and MICINN (Spain) Project No. PID2019-107396GBI00/AEI/10.13039/501100011033. We acknowledge financial support from Secretaría d’Universitats i Recerca del Departament d’Empresa i Coneixement de la Generalitat de Catalunya, cofunded by the European Union Regional Development Fund within the ERDF Operational Program of Catalunya (project QuantumCat, ref. 001-P-001644). V.C. acknowledges financial support from the Project HPC-EUROPA3 (INFRAIA-2016-1-730897), with the support of the EC Research Innovation Action under the H2020 Programme. J.S-B. acknowledges the FPU fellowship with reference FPU15/01805 from MCIU (Spain).