Momentum Distribution and Renormalization Factor in Sodium and the Electron Gas

Huotari, Simo; Soininen, J. A.; Pylkkänen, Tuomas; Hämäläinen, K.; Issolah, A.; Titov, A. A.; McMinis, Jeremy; Kim, Jeongnim; Esler, K.; Ceperley, David M.; Holzmann, Markus; Olevano, Valério

doi:10.1103/physrevlett.105.086403

Cited by 77 publications

(74 citation statements)

References 23 publications

(45 reference statements)

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“…a working condition similar to that of X-ray Compton scattering [49]. The value for the kinetic energy derived from the fit is hE K ðT ¼ 5KÞi = (150.87AE1.50) meV, higher than the calculation of 144 meV and a previous experimental determination [ As shown in the Introduction Section, there are two main approaches for the theoretical evaluation of hE K ðTÞi.…”

Section: Resultsmentioning

confidence: 92%

Temperature dependence of the zero point kinetic energy in ice and water above room temperature

2013

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a b s t r a c tBy means of Deep Inelastic Neutron Scattering we determined the temperature dependence of the proton kinetic energy in polycrystalline ice Ih between 5 K and 271 K. We compare our results with predictions form Path Integral quantum simulations and semiclassical quasi-harmonic models with phasedependent frequencies. The latter show the best agreement with the experiment if the librational contribution is properly taken into account. The kinetic energy increase with temperature in ice is also found to be approximately a factor $ 5 smaller than in the case of liquid water above room temperature, highlighting the role played by anharmonic quantum fluctuations in the two phases.

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Section: Resultsmentioning

confidence: 92%

Temperature dependence of the zero point kinetic energy in ice and water above room temperature

2013

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“…This work lead to explicit formulae for the finite size corrections to the energy and the pressure that are quite accurate in practice (Chiesa et al, 2006;Drummond et al, 2008). The method has been extended to the Fermi-liquid parameters in the homogeneous electron gas (Holzmann et al, 2011), and the renormalization factor of sodium (Huotari et al, 2010). Size effects can also affect structural properties of the ions as the following two examples illustrate.…”

Section: F Size Effectsmentioning

confidence: 99%

The properties of hydrogen and helium under extreme conditions

McMahon¹,

Morales²,

Pierleoni³

et al. 2012

Rev. Mod. Phys.

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478

415

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Hydrogen and helium are the most abundant elements in the universe and, in principle, are the simplest elements. Nonetheless, they display remarkable properties under pressure that have fascinated theoreticians and experimentalists for over a century. Recent advances in computational methods have made it possible to elucidate many of these properties. We review some of the computational methods that have been applied to dense hydrogen and helium in recent years, mainly those that perform a simulation directly from the physical picture of electrons and ions; primarily, those based on density functional theory and quantum Monte Carlo methods. We then discuss the predictions from such methods as applied to the phase diagram of hydrogen, including the solid and fluid phases, with particular focus on the crystal structures, the liquidliquid transition and comparison of the results with experimental shock-wave data. We then discuss predictions of ordered quantum states, including a possible low-temperature fluid and high-temperature superconductivity in the atomic state. We also briefly discuss pure helium, and then focus on hydrogen-helium mixtures, with particular focus on properties of relevance to planetary science.

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“…These results are widely regarded as the best estimates of energies in the HEG over a range of densities. DMC has allowed for a large range of properties of the electron gas to be calculated, including phase diagrams 17,39 , the effective mass 7,40 , the renomalization factor 41 , spectral moments 42 and the momentum distribution 5,43,44 . Unfortunately, since to the best knowledge of the authors no low-N simulations exist in the literature for DMC, comparison between FCIQMC energies and DMC are left largely as an open question.…”

Section: Application To the Hegmentioning

confidence: 99%

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models

Shepherd

Booth

Alavi

2012

The Journal of Chemical Physics

107

143

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Using the homogeneous electron gas (HEG) as a model, we investigate the sources of error in the 'initiator' adaptation to Full Configuration Interaction Quantum Monte Carlo (i -FCIQMC), with a view to accelerating convergence. In particular we find that the fixed shift phase, where the walker number is allowed to grow slowly, can be used to effectively assess stochastic and initiator error. Using this approach we provide simple explanations for the internal parameters of an i -FCIQMC simulation. We exploit the consistent basis sets and adjustable correlation strength of the HEG to analyze properties of the algorithm, and present finite basis benchmark energies for N = 14 over a range of densities 0.5 ≤ rs ≤ 5.0 a.u. A single-point extrapolation scheme is introduced to produce complete basis energies for 14, 38 and 54 electrons. It is empirically found that, in the weakly correlated regime, the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds. We expect the fixed shift strategy to reduce the computational cost of many i -FCIQMC calculations of weakly correlated systems. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.

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Momentum Distribution and Renormalization Factor in Sodium and the Electron Gas

Cited by 77 publications

References 23 publications

Temperature dependence of the zero point kinetic energy in ice and water above room temperature

Temperature dependence of the zero point kinetic energy in ice and water above room temperature

The properties of hydrogen and helium under extreme conditions

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models

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