Static response from quantum Monte Carlo calculations

Moroni, Saverio; Ceperley, David M.; Senatore, G.

doi:10.1103/physrevlett.69.1837

Cited by 163 publications

(175 citation statements)

References 20 publications

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“…We have followed the method used by Moroni et al [30], extending the calculations to more densities to better study the pressure dependence of χ(q). The simulation is carried out introducing in the Hamiltonian of the system an external potential inducing a modulation of the density,…”

Section: Direct Calculationsmentioning

confidence: 99%

Static Structure Factor and Static Response Function of Superfluid Helium 4: a Comparative Analysis

Caupin¹,

Boronat

Andersen

2008

J Low Temp Phys

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Extensive neutron scattering data on liquid helium 4 are available, and have been analyzed to give a number of physical quantities, e.g. static structure factor S(q), excitation energy, and roton linewidth. X-rays also give access to S(q). However, a comprehensive comparison between experimental data and theoretical results, including their dependence on pressure, is still lacking. The static response function χ(q) has been particularly overlooked, despite its fundamental role in theories of inhomogeneous helium. We present here a critical review about the strength of the main peaks of S(q) and χ(q). We include in the comparison the analysis of unpublished neutron data and new Monte-Carlo calculations of χ(q). We find a significant discrepancy between experiments, and suggest corrections which account for some of the differences. We give recommendations for the best values to use for S(q) and χ(q).

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Section: Direct Calculationsmentioning

confidence: 99%

Static Structure Factor and Static Response Function of Superfluid Helium 4: a Comparative Analysis

Caupin¹,

Boronat

Andersen

2008

J Low Temp Phys

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“…In particular, both the static spin-symmetric 8 and spin-antisymmetric 9 many-body local field factors have been obtained for the two-dimensional electron liquid. On the other hand, in view of the magnitude of the numerical effort required, only the corresponding spin-symmetric quantity has been obtained for the three-dimensional case.…”

Section: Introductionmentioning

confidence: 99%

“…1 Quantum Monte Carlo based numerical studies offer an alternative route and have the advantage of a theoretical framework that is accurate and virtually exact for a wide range of densities. [6][7][8][9][10] Despite intensive efforts, a quantitative characterization of the Fermi liquid regime in the intermediate density range is still to be achieved. In the case of the three-dimensional electron liquid, following a route originally proposed by Hubbard,11 vertex corrections were approximately incorporated to this purpose by Rice 12 through the use of a static many-body local field factor in an attempt to go beyond the random phase approximation ͑RPA͒ of Hedin and Lundqvist 13 and Quinn and Ferrell.…”

Section: Introductionmentioning

confidence: 99%

Many-body local fields theory of quasiparticle properties in a three-dimensional electron liquid

Simion

Giuliani

2008

Phys. Rev. B

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We present a quantitative study of the quasiparticle properties of a three-dimensional electron Fermi liquid. Our approach is based on the theory of the many-body local field factors which we use to include vertex corrections associated with charge and spin fluctuations. Extensive use is made of the results of recent quantum Monte Carlo calculations. Several models for the wave-vector dependence of the spin-antisymmetric manybody local field factor G − , for which no numerical results are currently available, are discussed and compared. Both the real and imaginary parts of the self-energy as well as the quasiparticle renormalization constant and the enhancement of the effective mass are calculated in the experimentally accessible range of electron densities. The results obtained by means of the on-shell approximation are critically compared with those given by a self-consistent solution of the Dyson equation. An ultraviolet catastrophe in the Coulomb-hole part of the self-energy is identified and a satisfactory resolution of this impasse is presented. The same many-body local field factors are also used to obtain the Landau interaction function. This allows us to obtain both the spin susceptibility and the proper compressibility of the system.

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“…[10] in such a way as to obtain analytical expressions for both K xc (q) and K xc (r). Our formula for G + (q) reads…”

mentioning

confidence: 99%

Analytical expressions for the charge-charge local-field factor and the exchange-correlation kernel of a two-dimensional electron gas

et al. 2001

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We present an analytical expression for the static many-body local field factor G+(q) of a homogeneous two-dimensional electron gas, which reproduces Diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small and large wave number q. This allows us to also provide a closed-form expression for the exchange and correlation kernel Kxc(r), which represents a key input for density functional studies of inhomogeneous systems.PACS number: 71.10. Ca, 71.15.Mb The static charge-charge response function χ C (q) of a paramagnetic electron gas (EG) can be written in terms of the Lindhard function χ 0 (q) by means of the spin-symmetric many-body local field G + (q) through the relationshipThus G + (q) is a fundamental quantity for the determination of many properties of a general electron system. By definition G + (q) is meant to represent the effects of the exchange and correlation hole surrounding each electron in the fluid and is therefore a key input in the density functional theory (DFT) of the inhomogeneous electron gas 1 and in studies of quasiparticle properties (such as the effective mass and the effective Landè g-factor) in the electronic Fermi liquid 2 . For what concerns DFT calculations, a common approximation to the unknown exchange-correlation energy functional E xc [n] appeals to its second functional derivative,wheren is the average local density of the EG. The local field factor and the exchange-correlation kernel are simply related in Fourier transform bywhere d is the dimensionality of the system and v q is the Fourier transform of the Coulomb potential e 2 /r. In what follows we shall only consider the case of two spatial dimensions, with d = 2 and v q = 2πe 2 /q. The corresponding three-dimensional case was discussed in Ref. [3]. A number of exact asymptotic properties of the static local field factor in two dimensions are readily proven. In particular,withwhere k F = √ 2πn = √ 2/r s a B is the Fermi wave number, r s = πna 2 B is the usual EG density parameter with a B the Bohr radius, κ 0 = πr 4 s /2 is the compressibility of the ideal gas in units of a 2 B /Ryd, while κ is the compressibility of the interacting system. By making use of the thermodynamic definition of κ we can write1 where ǫ c (r s ) is the correlation energy per particle. Once this function is known, it is possible to calculate A + . For the present purpose ǫ c (r s ) can be taken from the Monte Carlo data of Ref. [4]. The asymptotic behavior of G + (q) at large q is also known exactly 5,6 :where C + is proportional to the difference in kinetic energy between the interacting and the ideal gas,Moreover B + = 1 − g(0), g(0) being the value of the pair-correlation function at the origin. For g(0) we use the simple expressionwhich has been derived 7 by an interpolation between the result of a low-r s expansion, including the second order direct and exchange contributions to the energy in the paramagnetic state, and the result of a partial-wave phase-shift analysis near Wigner crystallization. This interpolatio...

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Static response from quantum Monte Carlo calculations

Cited by 163 publications

References 20 publications

Static Structure Factor and Static Response Function of Superfluid Helium 4: a Comparative Analysis

Static Structure Factor and Static Response Function of Superfluid Helium 4: a Comparative Analysis

Many-body local fields theory of quasiparticle properties in a three-dimensional electron liquid

Analytical expressions for the charge-charge local-field factor and the exchange-correlation kernel of a two-dimensional electron gas

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