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Universality of quantum halo states enables comparison of systems from different fields of physics, as demonstrated in two-and three-body clusters. In the present work, we studied weakly-bound helium tetramers in order to test whether some of these four-body realistic systems qualify as halos. Their ground-state binding energies and structural properties were thoroughly estimated using the diffusion Monte Carlo method with pure estimators. Helium tetramer properties proved to be less sensitive on the potential model than previously evaluated trimer properties. We predict the existence of the realistic four-body halo 4 He 2 3 He 2 , while 4 He 4 and 4 He 3 3 He are close to the border and thus can be used as prototypes of quasi-halo systems. Our results could be tested by experimental determination of tetramers' structural properties, using a similar setup to the one developed for the study of helium trimers.

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“…32 We first present the selected interaction potential models and then discuss the basic features of the method.…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…32 For the mean square root of pair distances r ij , density profiles ρ(r) and the pair distributions functions P (r) and P 2 (r ij , r kl )…”

Section: Dmc Methods Solves Stochastically the Schrödinger Equation Wrmentioning

confidence: 99%

Quantum Halo States in Helium Tetramers

2016

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“…Nevertheless, expectation values obtained with the extrapolation approach never are totally free of bias, and it is difficult to estimate a priori the size of the accompanying errors. In order to overcome such limitations, one can calculate "pure" expectation values (that is, exact to within the statistical errors) by using the forward walking technique (Casulleras and Boronat, 1995).…”

Section: Diffusion Monte Carlomentioning

confidence: 99%

Simulation and understanding of atomic and molecular quantum crystals

2017

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Quantum crystals abound in the whole range of solid-state species. Below a certain threshold temperature the physical behavior of rare gases ( 4 He and Ne), molecular solids (H 2 and CH 4 ), and some ionic (LiH), covalent (graphite), and metallic (Li) crystals can be only explained in terms of quantum nuclear effects (QNE). A detailed comprehension of the nature of quantum solids is critical for achieving progress in a number of fundamental and applied scientific fields like, for instance, planetary sciences, hydrogen storage, nuclear energy, quantum computing, and nanoelectronics. This review describes the current physical understanding of quantum crystals formed by atoms and small molecules, as well as the wide palette of simulation techniques that are used to investigate them. Relevant aspects in these materials such as phase transformations, structural properties, elasticity, crystalline defects and the effects of reduced dimensionality, are discussed thoroughly. An introduction to quantum Monte Carlo techniques, which in the present context are the simulation methods of choice, and other quantum simulation approaches (e. g., path-integral molecular dynamics and quantum thermal baths) is provided. The overarching objective of this article is twofold. First, to clarify in which crystals and physical situations the disregard of QNE may incur in important bias and erroneous interpretations. And second, to promote the study and appreciation of QNE, a topic that traditionally has been treated in the context of condensed matter physics, within the broad and interdisciplinary areas of materials science.

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“…DMC density profiles and S(k) are calculated using the technique of pure estimators. 16 The typical kinetic energy per particle scales quadratically with the density, opposite to the linear density dependence in the Coulomb interaction energy. At high densities the kinetic energy becomes dominant and can be approximated by the energy of an ideal Fermi gas (IFG):…”

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confidence: 99%

Exact ground-state properties of a one-dimensional Coulomb gas

Astrakharchik

Girardeau

2011

Phys. Rev. B

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The ground-state properties of a single-component one-dimensional Coulomb gas are investigated. We use Bose-Fermi mapping for the ground-state wave function which permits solution of the Fermi sign problem in the following respects: (i) the nodal surface is known, permitting exact calculations; and (ii) evaluation of determinants is avoided, reducing the numerical complexity to that of a bosonic system and, thus, allowing simulation of a large number of fermions. Due to the mapping, the energy and local properties in one-dimensional Coulomb systems are exactly the same for Bose-Einstein and Fermi-Dirac statistics. The exact ground-state energy is calculated in homogeneous and trapped geometries using the diffusion Monte Carlo method. We show that in the low-density Wigner crystal limit an elementary low-lying excitation is a plasmon, which is to be contrasted with the high-density ideal Fermi gas/Tonks-Girardeau limit, where low-lying excitations are phonons. Exact density profiles are compared to the ones calculated within the local density approximation, which predicts a change from a semicircular to an inverted parabolic shape of the density profile as the value of the charge is increased. The recent progress in nanoscale technology has made it possible to realize clean one-dimensional quantum gases, such as ultracold atoms confined in elongated traps 1 and electrons in single-well carbon nanotubes 2 and in semiconductor quantum wires. 3 A peculiarity of a one-dimensional world is that such systems can be explained not by the conventional Landau theory of normal Fermi liquids but, rather, by an effective low-energy Luttinger liquid description, 4 generalizable to long-range Coulomb interactions. 5 A number of approaches of increasing accuracy (random-phase approximation, SingwiTosi-Land-Sjölander scheme, density functional theory) have been devised to study energetic and structural properties. 6 The most precise calculations of energy have been obtained by the Monte Carlo technique as in Ref. 7, where a quasi-onedimensional geometry with a finite width of the transverse confinement is studied. The purpose of the present work is to carry out exact calculations in a strictly one-dimensional geometry.In this paper we use the Bose-Fermi mapping to find the ground-state energy of a one-dimensional single-component Coulomb system exactly within statistical precision. The mapping applies to both homogeneous and trapped geometries.We consider a single-component system of N particles (bosons or fermions) of charge e and mass m in a onedimensional box of length L. Periodic boundary conditions are applied and the Coulomb potential is truncated for interparticle distances larger than L/2. The Hamiltonian readŝNatural length scales in a homogeneous system are defined by atomic units, that is, the Bohr radius a 0 =h 2 /me 2 for length and the Rydberg number Ry = e 2 /2a 0 for energy. The system properties are governed by a single parameter, fixed by the ratio of Bohr a 0 radius and Wigner-Seitz r s = 1/2n radius or, equiva...

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Unbiased estimators in quantum Monte Carlo methods: Application to liquidHe4

Cited by 150 publications

References 23 publications

Quantum Halo States in Helium Tetramers

Quantum Halo States in Helium Tetramers

Simulation and understanding of atomic and molecular quantum crystals

Exact ground-state properties of a one-dimensional Coulomb gas

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