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.

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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...