246 research outputs found
First-principles modeling of three-body interactions in highly compressed solid helium
We present a new set of three-body interaction models based on the
Bruch-McGee (BM) potential that are suitable for the study of the energy,
structural and elastic properties of solid 4He at high pressure. Our ab initio
three-body potentials are obtained from the fit to total energies and atomic
forces computed with the van der Waals density functional theory method due to
Grimme, and represent an improvement with respect to previously reported
three-body interaction models. In particular, we show that some of the
introduced BM parametrizations reproduce closely the experimental equation of
state and bulk modulus of solid helium up to a pressure of ~ 60 GPa, when used
in combination with standard pairwise interaction models in diffusion Monte
Carlo simulations. Importantly, we find that recent predictions reporting a
surprisingly small variation of the kinetic energy and Lindeman ratio on
quantum crystals under increasing pressure are likely to be artifacts produced
by the use of incomplete interaction models. Also, we show that the
experimental variation of the shear modulus, C44, at P < 25 GPa can be
quantitatively described with the new set of three-body BM potentials. At
higher pressures, however, the agreement between our C44 results and
experiments deteriorates and thus we argue that higher order many-body terms in
the expansion of the atomic interactions probably are necessary in order to
better describe elasticity in very dense solid 4He.Comment: 11 pages, 7 figure
Possible superfluidity of molecular hydrogen in a two-dimensional crystal phase of sodium
We theoretically investigate the ground-state properties of a molecular
para-hydrogen (p-H2) film in which crystallization is energetically frustrated
by embedding sodium (Na) atoms periodically distributed in a triangular
lattice. In order to fully deal with the quantum nature of p-H2 molecules, we
employ the diffusion Monte Carlo method and realistic semi-empirical pairwise
potentials describing the interactions between H2-H2 and Na-H2 species. In
particular, we calculate the energetic, structural and superfluid properties of
two-dimensional Na-H2 systems within a narrow density interval around
equilibrium at zero temperature. In contrast to previous computational studies
considering other alkali metal species such as rubidium and potassium, we find
that the p-H2 ground-state is a liquid with a significantly large superfluid
fraction of ~30%. The appearance of p-H2 superfluid response is due to the fact
that the interactions between Na atoms and H2 molecules are less attractive
than between H2 molecules. This induces a considerable reduction of the
hydrogen density which favours the stabilization of the liquid phase.Comment: 7 pages, 6 figures, submitte
The Limit of Mechanical Stability in Quantum Crystals: A Diffusion Monte Carlo Study of Solid 4He
We present a first-principles study of the energy and elastic properties of
solid helium at pressures below the range in which is energetically stable. We
find that the limit of mechanical stability in hcp 4He is = -33.82 bar,
which lies significantly below the spinodal pressure found in the liquid phase
(i.e., -9.6 bar). Furthermore, we show that the pressure variation of the
transverse and longitudinal sound velocities close to do not follow a
power law of the form , in contrast
to what is observed on the fluid.Comment: 4 pages, 4 figure
Temperature Dependence of the Vacancy Formation Energy in Solid He
We studied the thermal effects on the behavior of incommensurate solid He
at low temperatures using the path integral Monte Carlo method. Below a certain
temperature, depending on the density and the structure of the crystal, the
vacancies delocalize and a finite condensate fraction appears. We calculated
the vacancy formation energy as a function of the temperature and observed a
behavior compatible with a two-step structure, with a gap of few K appearing at
the onset temperature of off-diagonal long-range order. Estimation of the
energy cost of creating two vacancies seems to indicate an effective attractive
interaction among the vacancies but the large error inherent to its numerical
estimation precludes a definitive statement.Comment: Contribution to the Special Issue on "Quantum Crystals": 9 pages, 3
figure
Luttinger-liquid behavior of one-dimensional He-3
The ground-state properties of one-dimensional He-3 are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well interpolated by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation functions. The density dependence of the Luttinger parameter is explicitly found, and interestingly it shows a nonmonotonic behavior. Depending on the density, the static structure factor can be a smooth function of the momentum or might contain a peak of a finite or infinite height. Although no phase transitions are present in the system, we identify a number of physically different regimes, including an ideal Fermi gas, aPostprint (published version
First-principles modeling of quantum nuclear effects and atomic interactions in solid He-4 at high pressure
We present a first-principles computational study of solid He-4 at T = 0 K and pressures up to similar to 160 GPa. Our computational strategy consists in using van der Waals density functional theory (DFT-vdW) to describe the electronic degrees of freedom in this material, and the diffusion Monte Carlo (DMC) method to solve the Schrodinger equation describing the behavior of the quantum nuclei. For this, we construct an analytical interaction function based on the pairwise Aziz potential that closely matches the volume variation of the cohesive energy calculated with DFT-vdW in dense helium. Interestingly, we find that the kinetic energy of solid He-4 does not increase appreciably with compression for P >= 85 GPa. Also, we show that the Lindemann ratio in dense solid He-4 amounts to 0.10 almost independently of pressure. The reliability of customary quasiharmonic DFT (QH DFT) approaches in describing quantum nuclear effects in solids is also studied. We find that QH DFT simulations, although provide a reasonable equation of state in agreement with experiments, are not able to reproduce correctly these critical effects in compressed He-4. In particular, we disclose huge discrepancies of at least similar to 50% in the calculated He-4 kinetic energies using both the QH DFT and present DFT-DMC methods.Postprint (published version
Low-energy scattering parameters: A theoretical derivation of the effective range and scattering length for arbitrary angular momentum
The most important parameters in the study of low-energy scattering are the
s-wave and p-wave scattering lengths and the s-wave effective range. We solve
the scattering problem and find two useful formulas for the scattering length
and the effective range for any angular momentum, as long as the Wigner
threshold law holds. Using that formalism, we obtain a set of useful formulas
for the angular-momentum scattering parameters of four different model
potentials: hard-sphere, soft-sphere, spherical well, and well-barrier
potentials. The behavior of the scattering parameters close to Feshbach
resonances is also analyzed. Our derivations can be useful as hands-on
activities for learning scattering theory.Comment: Main document with two supplementary material
Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function
We present a method based on the Path Integral Monte Carlo formalism for the
calculation of ground-state time correlation functions in quantum systems. The
key point of the method is the consideration of time as a complex variable
whose phase acts as an adjustable parameter. By using high-order
approximations for the quantum propagator, it is possible to obtain Monte Carlo
data all the way from purely imaginary time to values near the limit
of real time. As a consequence, it is possible to infer accurately the spectral
functions using simple inversion algorithms. We test this approach in the
calculation of the dynamic structure function of two
one-dimensional model systems, harmonic and quartic oscillators, for which
can be exactly calculated. We notice a clear improvement in the
calculation of the dynamic response with respect to the common approach based
on the inverse Laplace transform of the imaginary-time correlation function.Comment: Accepted for publication on "Jornal of Chemical Physics
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