We have extracted information about real time dynamics of H4e systems from noisy imaginary-time correlation functions f($\tau${}) computed via quantum Monte Carlo (QMC): production and falsification of model spectral functions s($\omega${}) are obtained via a survival-to-compatibility with f($\tau${}) evolutionary process, based on genetic algorithms. Statistical uncertainty in f($\tau${}) is promoted to be an asset via a sampling of equivalent f($\tau${}) within the noise, which give rise to independent evolutionary processes. In the case of pure superfluid H4e we have recovered from exact QMC simulations sharp quasiparticle excitations with spectral functions displaying also the multiphonon branch. As further applications, we have studied the impuriton branch of one H3e atom in liquid H4e and the vacancy-wave excitations in hcp solid H4e finding an unexpected rotonlike feature.

We compute the zero-temperature dynamical structure factor of one-dimensional liquid ${}^4\mathrm{He}$ by means of state-of-the-art quantum Monte Carlo and analytic continuation techniques. By increasing the density, the dynamical structure factor reveals a transition from a highly compressible critical liquid to a quasisolid regime. In the low-energy limit, the dynamical structure factor can be described by the quantum hydrodynamic Luttinger-liquid theory, with a Luttinger parameter spanning all possible values by increasing the density. At higher energies, our approach provides quantitative results beyond the Luttinger-liquid theory. In particular, as the density increases, the interplay between dimensionality and interaction makes the dynamical structure factor manifest a pseudo-particle-hole continuum typical of fermionic systems. At the low-energy boundary of such a region and moderate densities, we find consistency, within statistical uncertainties, with predictions of a power-law structure by the recently developed nonlinear Luttinger-liquid theory. In the quasisolid regime, we observe a novel behavior at intermediate momenta, which can be described by new analytical relations that we derive for the hard-rods model.

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 nonzero overlap with the ground state, which 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 H4e 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 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.

We study with variational Monte Carlo simulations a single ion impurity in nanodroplets and in liquid ${}^4\mathrm{He}$. Within the shadow wave function (SWF) approach we have studied alkali-earth ion doped ${}^4\mathrm{He}$ systems (${\mathrm{Be}}^{+}$ and ${\mathrm{Mg}}^{+}$) and we have also improved our previous variational results for alkali ion impurities (${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, and ${\mathrm{Cs}}^{+}$). The new $\mathrm{SWF}$ allows for anisotropic correlations between ${}^4\mathrm{He}$ atoms and the ion. The first shell of ${}^4\mathrm{He}$ atoms around the ions has always a well defined solidlike structure, which is remarkably different for each ion but it does not depend on the ${}^4\mathrm{He}$ system (bulk liquid or cluster). We also give results for the chemical potential, the single particle excitation spectrum, and the effective mass of the ions in the bulk.

Graphical Abstract Abstract The term analytic continuation emerges in many branches of Mathematics, Physics, and, more generally, applied Science. Generally speaking, in many situations, given some amount of information that could arise from experimental or numerical measurements, one is interested in extending the domain of such information, to infer the values of some variables which are central for the study of a given problem. For example, focusing on Condensed Matter Physics, state-of-the-art methodologies to study strongly correlated quantum physical systems are able to yield accurate estimations of dynamical correlations in imaginary time. Those functions have to be extended to the whole complex plane, via analytic continuation, in order to infer real-time properties of those physical systems. In this review, we will present the Genetic Inversion via Falsification of Theories method, which allowed us to compute dynamical properties of strongly interacting quantum many–body systems with very high accuracy. Even though the method arose in the realm of Condensed Matter Physics, it provides a very general framework to face analytic continuation problems that could emerge in several areas of applied Science. Here, we provide a pedagogical review that elucidates the approach we have developed.