Study of a 2D Bose-Fermi mixture with quantum Monte Carlo methods

Ultracold gases are an exceptionally versatile platform to test novel physical concepts. Thanks to the development of new experimental techniques, they have greatly advanced our understanding of the physics of many-body systems and allowed precision measurements of fundamental constants. Bose-Fermi mixtures can then be introduced in this context. This novel quantum many-body system is essentially an ultracold gas made up by both bosons and fermions, where tunable attractive or repulsive interactions between the components can be introduced. At T = 0 and for weak interactions the bosons condense while the fermions behave as a Fermi liquid. In particular, a recent system of interest is given by two-dimensional Bose-Fermi mixtures with both Bose-Fermi and Bose-Bose repulsive interactions. In the present work, a Quantum Monte Carlo study is conducted, for a fixed value of boson concentration, at zero-temperature from the weak to the strong Bose-Fermi coupling limit. Variational Monte Carlo and Fixed-Node Diffusion Monte Carlo are applied using an optimized Jastrow-Slater wavefunction, extending previous methodology developed for the three-dimensional case. The results are then compared with perturbative predictions, showing very good agreement in the weak coupling region. Variational Monte Carlo agrees with the analytic predictions only for extremely weak coupling, while Diffusion Monte Carlo proves necessary to recover good agreement over the whole perturbative regime. For stronger couplings, our simulations indicate the tendency of the mixture to form bosonic clusters. This finding would definitively deserve further investigation, which is postponed to future works.