We have extracted information about real time dynamics of 4 He systems from noisy imaginary time correlation functions f (τ ) computed via Quantum Monte Carlo (QMC): production and falsification of model spectral functions s(ω) are obtained via a survival-to-compatibility with f (τ ) evolutionary process, based on Genetic Algorithms. Statistical uncertainty in f (τ ) is promoted to be an asset via a sampling of equivalent f (τ ) within the noise, which give rise to independent evolutionary processes. In the case of pure superfluid 4 He we have recovered from exact QMC simulations sharp quasi-particle excitations with spectral functions displaying also the multiphonon branch. As further applications, we have studied the impuriton branch of one 3 He atom in liquid 4 He and the vacancy-wave excitations in hcp solid 4 He finding a novel roton like feature.

We compute the zero-temperature dynamical structure factor of one-dimensional liquid 4 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. DOI: 10.1103/PhysRevLett.116.135302 One-dimensional (1D) quantum systems exhibit some of the most diverse and fascinating phenomena of condensed matter physics [1][2][3]. Among the most spectacular signatures of the interplay between quantum fluctuations, interaction and reduced dimensionality, are the breakdown of ordered phases in the presence of short-range interactions [4] and the loosened distinction between Bose and Fermi behavior [5]. The study of quasi-1D quantum systems is a very active research field, aroused by the experimental investigation of electronic transport properties [6][7][8][9][10], by the fabrication of long 1D arrays of Josephson junctions [11], and recently corroborated by the availability of ultracold atomic gases in highly anisotropic traps and optical lattices [2,[12][13][14], as well as by experiments on confined He atoms [15][16][17][18][19].The low-energy properties of a wide class of Bose and Fermi 1D quantum systems [1,20] are notoriously captured by the phenomenological Tomonaga-Luttinger-liquid (TLL) theory [21][22][23], characterized by collective phononlike excitations. This theory introduces two conjugate Bose fields ϕðxÞ and θðxÞ describing, respectively, the density and phase fluctuations of the field operator ψðxÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ρ þ ∂ x ϕðxÞ p e iθðxÞ , where ρ is the average density. Those fields are described by the exactly solvable lowenergy effective Hamiltonian:Although, in general, the TLL parameter K L and the sound velocity c are independent quantities (notably in lattice models), for Galilean-invariant systems c ¼ v F =K L [23], v F ¼ ℏk F =m being the Fermi velocity and k F ¼ πρ the Fermi wave vector of a 1D ideal Fermi gas (IFG), and K L is thus related to the compressibility κ S by mK 2 L ¼ ℏ 2 π 2...

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.

Path integral Monte Carlo calculations of (4)He nanodroplets doped with alkali (Na(+), K(+) and Cs(+)) and alkali-earth (Be(+) and Mg(+)) ions are presented. We study the system at T = 1 K and between 14 and 128 (4)He atoms. For all studied systems, we find that the ion is well localized at the center of the droplet with the formation of a "snowball" of well-defined shells of localized (4)He atoms forming solid-like order in at least the first surrounding shell. The number of surrounding helium shells (two or three) and the number of atoms per shell and the degree of localization of the helium atoms are sensitive to the type of ion. The number of (4)He atoms in the first shell varies from 12 for Na(+) to 18 for Mg(+) and depends weakly on the size of the droplet. The study of the density profile and of the angular correlations shows that the local solid-like order is more pronounced for the alkali ions with Na(+) giving a very stable icosahedral order extending up to three shells.

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