Generally "exact" Quantum Monte Carlo computations for the ground state of many Bosons make use of importance sampling. The importance sampling is based, either on a guiding function or on an initial variational wave function. Here we investigate the need of importance sampling in the case of Path Integral Ground State (PIGS) Monte Carlo. PIGS is based on a discrete imaginary time evolution of an initial wave function with a non zero overlap with the ground state, that gives rise to a discrete path which is sampled via a Metropolis like algorithm. In principle the exact ground state is reached in the limit of an infinite imaginary time evolution, but actual computations are based on finite time evolutions and the question is whether such computations give unbiased exact results. We have studied bulk liquid and solid 4 He with PIGS by considering as initial wave function a constant, i.e. the ground state of an ideal Bose gas. This implies that the evolution toward the ground state is driven only by the imaginary time propagator, i.e. there is no importance sampling. For both the phases we obtain results converging to those obtained by considering the best available variational wave function (the Shadow wave function) as initial wave function. Moreover we obtain the same results even by considering wave functions with the wrong correlations, for instance a wave function of a strongly localized Einstein crystal for the liquid phase. This convergence is true not only for diagonal properties such as the energy, the radial distribution function and the static structure factor, but also for off-diagonal ones, such as the one-body density matrix. This robustness of PIGS can be traced back to the fact that the chosen initial wave function acts only at the beginning of the path without affecting the imaginary time propagator. From this analysis we conclude that zero temperature PIGS calculations can be as unbiased as those of finite temperature Path Integral Monte Carlo. On the other hand, a judicious choice of the initial wave function greatly improves the rate of convergence to the exact results.

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By means of the exact Path Integral Monte Carlo method we have performed a detailed microscopic study of 4 He nanodroplets doped with an argon ion, Ar + , at T = 0.5 K. We have computed density profiles, energies, dissociation energies and characterized the local order around the ion for nanodroplets with a number of 4 He atoms ranging from 10 to 64 and also 128. We have found the formation of a stable solid structure around the ion, a "snowball", consisting of 3 concentric shells in which the 4 He atoms are placed on at the vertices of platonic solids: the first inner shell is an icosahedron (12 atoms); the second one is a dodecahedron with 20 atoms placed on the faces of the icosahedron of the first shell; the third shell is again an icosahedron composed of 12 atoms placed on the faces of the dodecahedron of the second shell. The "magic numbers" implied by this structure, 12, 32 and 44 helium atoms, have been observed in a recent experimental study [1] of these complexes; the dissociation energy curve computed in the present work shows jumps in correspondence with those found in the nanodroplets abundance distribution measured in that experiment, strengthening the agreement between theory and experiment. The same structures were predicted in Ref.[2] in a study regarding Na + @ 4 He n when n > 30; a comparison between Ar + @ 4 He n and Na + @ 4 He n complexes is also presented.

We report a quantitative experimental study of the crystallization kinetics of supercooled quantum liquid mixtures of parahydrogen (pH 2 ) and orthodeuterium (oD 2 ) by high spatial resolution Raman spectroscopy of liquid microjets. We show that in a wide range of compositions the crystallization rate of the isotopic mixtures is significantly reduced with respect to that of the pure substances. To clarify this behavior we have performed path-integral simulations of the nonequilibrium pH 2 -oD 2 liquid mixtures, revealing that differences in quantum delocalization between the two isotopic species translate into different effective particle sizes. Our results provide experimental evidence for crystallization slowdown of quantum origin, offering a benchmark for theoretical studies of quantum behavior in supercooled liquids. Understanding the stability of supercooled liquids with respect to crystallization is a fundamental open problem in condensed matter physics [1]. In this regard, since crystallization competes with glass formation, a knowledge of the mechanisms that govern the crystal growth in supercooled liquids is considered an important step to elucidate the nature of the glass transition [2-6]. So far, experimental studies aiming at providing microscopic insights into the dynamics and crystallization of supercooled liquids have been largely based on the use of colloidal suspensions [7,8], where the large particle size allows one to follow the crystal growth on the laboratory time scale. However, diverse drawbacks such as polydispersity and sedimentation often make the experimental data from these systems difficult to interpret [8,9]. Accessing the details of the crystallization process in simple atomic and molecular counterparts, on the other hand, remains an experimental challenge due to relevant time scales that are orders of magnitude shorter.Theoretical studies have shown that the inclusion of quantum effects adds a further degree of complexity in the behavior of supercooled liquids, leading to novel exotic phenomena such as superfluidity [10,11] or enhanced dynamical slowing down [12][13][14]. Yet again, the difficulties in supercooling a quantum liquid to very low temperatures have so far precluded possible experimental studies of the interplay of quantum effects and structural transformations in nonequilibrium bulk liquids. Here we address these challenges reporting on the experimental investigation of the crystallization kinetics of supercooled liquid mixtures of the isotopic species pH 2 and oD 2 , showing that their quantum nature has a profound impact on the crystallization process.* grisenti@atom.uni-frankfurt.de Binary liquid mixtures exhibit, in general, properties that differ fundamentally from their corresponding pure substances, and mixing a few components is, in particular, a common strategy to hinder crystallization. Indeed, classical binary systems of particles that interact via a simple LennardJones (LJ) pair potential have been widely employed as the simplest theoretical models to inve...