We have studied dilute Bose-Bose mixtures of atoms with attractive interspecies and repulsive intraspecies interactions using quantum Monte Carlo methods at T = 0. Using a number of models for interactions, we determine the range of validity of the universal equation of state of the symmetric liquid mixture as a function of two parameters: the s-wave scattering length and the effective range of the interaction potential. It is shown that the Lee-Huang-Yang correction is sufficient only for extremely dilute liquids with the additional restriction that the range of the potential is small enough. Based on the quantum Monte Carlo equation of state we develop a new density functional which goes beyond the Lee-Huang-Yang term and use it together with local density approximation to determine density profiles of realistic self-bound drops.Dilute Bose and Fermi gases have proved to be a versatile tool for exploration of different phases of condensedmatter systems. For more than two decades, most of the experiments were done in the low-density gas phase, in the universal regime fixed solely by the gas parameter ρa 3 , with a the s-wave scattering length and ρ the density. The range of universality of the homogeneous Bose gas was established using different model potentials and solving the N -body problem in an exact way with quantum Monte Carlo (QMC) methods [1]. One of the most important advances in the field of ultracold atoms in the last years is the recent creation of ultradilute quantum droplets. Such self-bound quantum systems were first experimentally observed for dipolar atoms [3-6] being caused by a close cancellation of the dipolar and shortrange energies. Petrov [7] pointed out that liquid drops can be created in an even simpler setup composed by a two-component mixture of bosons with short-ranged attractive interspecies and repulsive intraspecies interactions. However, the perturbative technique employed by Petrov is valid only very close to the mean-field (MF) instability limit, that is for extremely dilute liquids. The collapse predicted on the MF level is avoided by stabilization due to the quantum fluctuations described by the Lee-Huang-Yang (LHY) correction to the energy. It was shown that a similar stabilization mechanism can be used in two-and one-dimensional geometries where the resulting liquid phase has enhanced stability [8]. Very recently, two experimental groups managed to obtain self-bound liquid drops [9, 10] which, upon releasing the trap, did not expand. The drops required a certain critical number of atoms to be bound. Importantly, measurements of the critical number and size of the smallest droplets could not be fully accounted for by the MF+LHY term [9].Recently, some of us have studied liquid Bose-Bose droplets by using the diffusion Monte Carlo (DMC) method, thus solving exactly the full many-body problem for a given Hamiltonian at zero temperature [11].Our results have confirmed the transition from a gas, with positive energy, to a self-bound droplet with negative energy. Furthermore, we ...

The ground state of weakly bound dimers and trimers with a radius extending well into the classically forbidden region is explored, with the goal to test the predicted universality of quantum halo states. The focus of the study is molecules consisting of T↓, D↓, ^{3}He, ^{4}He, and alkali atoms, where the interaction between particles is much better known than in the case of nuclei, which are traditional examples of quantum halos. The study of realistic systems is supplemented by model calculations in order to analyze how low-energy properties depend on the interaction potential. The use of variational and diffusion Monte Carlo methods enabled a very precise calculation of both the size and binding energy of the trimers. In the quantum halo regime, and for large values of scaled binding energies, all clusters follow almost the same universal line. As the scaled binding energy decreases, Borromean states separate from tango trimers.

Using quantum Monte Carlo methods we have studied dilute Bose-Bose mixtures with attractive interspecies interaction in the limit of zero temperature. The calculations are exact within some statistical noise and thus go beyond previous perturbative estimations. By tuning the intensity of the attraction, we observe the evolution of an N -particle system from a gas to a self-bound liquid drop. This observation agrees with recent experimental findings and allows for the study of an ultradilute liquid never observed before in Nature.

The ground-state properties of spin-polarized tritium T↓ at zero temperature are obtained by means of diffusion Monte Carlo calculations. Using an accurate ab initio T ↓ -T↓ interatomic potential we have studied its liquid phase, from the spinodal point until densities above its freezing point. The equilibrium density of the liquid is significantly higher and the equilibrium energy of −3.664͑6͒ K significantly lower than in previous approximate descriptions. The solid phase has also been studied for three lattices up to high pressures and we find that hcp lattice is slightly preferred. The liquid-solid phase transition has been determined using the double-tangent Maxwell construction; at zero temperature, bulk tritium freezes at a pressure of P =9͑1͒ bar.