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Journal of Physics Condensed Matter

Dielectric response of the degenerate plasma of charged bosons in static-local-field approximations

Sergio Conti, M. L. Chiofalo, Monica Tosi

Published Oct 17, 1994• 18 citations
Publisher

Abstract

The dielectric screening function epsilon (k, omega ) of the fluid of charged bosom at zero temperature is evaluated in a range of low-to-intermediate coupling strength, in view of recent data on static screening and fluid structure from quantum Monte Carlo methods. Correlations beyond the random phase approximation are included within a class of approximations which are well known for the electron fluid, i.e. by introducing a frequency-independent local field factor to be determined through self-consistency requirements connecting various aspects of the physics contained in the dielectric function. The static dielectric function epsilon (k,0) is negative over a range of wavenumbers at all values of the density, leading to oscillatory screening of a foreign charge and to an effective long-range attraction between equi-charged impurities. Quantitative agreement with the Monte Carlo data on static screening is achieved by imposing self-consistency on the compressibility of the fluid in addition to self-consistency on the pair distribution function. Good agreement is also obtained on the pair distribution function and the correlation energy. Within the present class of approximations, the dispersion relation of longitudinal excitations takes the Feynman form, starting at the plasma frequency with a negative dispersion coefficient and going through a minimum before ending at the single-particle recoil frequency.

DOI
10.1088/0953-8984/6/42/011

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quant-pharXiv:2610.06202•Oct 6, 2026
The dielectric screening function epsilon (k, omega ) of the fluid of charged bosom at zero temperature is evaluated in a range of low-to-intermediate coupling strength, in view of recent data on static screening and fluid structure from quantum Monte Carlo methods. Correlations beyond the random phase approximation are included within a class of approximations which are well known for the electron fluid, i.e. by introducing a frequency-independent local field factor to be determined through self-consistency requirements connecting various aspects of the physics contained in the dielectric function. The static dielectric function epsilon (k,0) is negative over a range of wavenumbers at all values of the density, leading to oscillatory screening of a foreign charge and to an effective long-range attraction between equi-charged impurities. Quantitative agreement with the Monte Carlo data on static screening is achieved by imposing self-consistency on the compressibility of the fluid in addition to self-consistency on the pair distribution function. Good agreement is also obtained on the pair distribution function and the correlation energy. Within the present class of approximations, the dispersion relation of longitudinal excitations takes the Feynman form, starting at the plasma frequency with a negative dispersion coefficient and going through a minimum before ending at the single-particle recoil frequency.
The diffusion Monte Carlo (DMC) method is used to analyze various properties of the three-dimensional plasma of charged bosons in the homogeneous fluid regime, over the density range 1\ensuremath{\le}rs{\mathit{r}}_{\mathit{s}}rs​\ensuremath{\le}160 extending from the so-called uniform limit (${\mathit{r}}_{\mathit{s}}1)tothecrystallinephase(1) to the crystalline phase (1)tothecrystallinephase({\mathit{r}}_{\mathit{s}}$\ensuremath{\gtrsim}160). The data on the static density response function \ensuremath{\chi}(k) extend to intermediate and high wave number k the work of Sugiyama, Bowen, and Alder [Phys. Rev. B 46, 13 042 (1992)] and allow us to extract the static local-field factor G(k) for exchange and correlation. The DMC results for the momentum distribution n(k) show that the condensate fraction decreases with increasing coupling strength from 83% at rs{\mathit{r}}_{\mathit{s}}rs​=1 to less than 1% at rs{\mathit{r}}_{\mathit{s}}rs​=160. We also present results for the ground-state energy Eg{\mathit{E}}_{\mathit{g}}Eg​(rs{\mathit{r}}_{\mathit{s}}rs​) and for the structure factor S(k). The results for Eg{\mathit{E}}_{\mathit{g}}Eg​(rs{\mathit{r}}_{\mathit{s}}rs​), n(k), and \ensuremath{\chi}(k) are summarized in analytic interpolation formulas embodying the known asymptotic behaviors. A rigorous upper bound on the plasmon dispersion curve is obtained from the DMC data through a sum-rule argument. \textcopyright{} 1996 The American Physical Society.
The dielectric function of a charged Bose gas is determined from the response to an imposed static sinusoidal electric field. Variational and diffusion quantum Monte Carlo simulations are used to calculate the ground-state properties of the system with trial wave functions containing a parameter dependent on the amplitude and wavelength of the perturbation. The induced charge is most efficiently extracted from the difference in ground-state energies at different magnitudes of the external field, rather than directly from the expectation value of the density fluctuation operator. Results are compared to the random-phase approximation for the weakly coupled fluid and to classical lattice values at low densities where the system forms a Wigner crystal. The dielectric function is also calculated at intermediate fluid densities and the transition from positive to negative response is found to occur in the metallic regime.
We briefly review the available theoretical results on dielectric screening properties of a fluid of charged bosons at zero temperature in comparison with those of a fluid of charged fermions. The paper is intended to highlight for the nonspecialists the differences in behavior that arise from the difference in statistics. After a general introduction to the dielectric screening function and to the local field factor accounting for exchange and correlation in dielectric screening, we focus on (i) the dependence of the static dielectric function on wave number and the screening of a charged impurity, (ii) the structure factor, the pair distribution function, and the ground state energy, and (iii) the spectrum of collective excitations. The review is concluded with some remarks on open questions and possible further developments.
The ground state of a charged Bose gas is studied throughout a large range of densities in a self-consistent-field approximation formalism which includes the short-range correlations between bosons through a local-field correction. Numerical self-consistent calculations have been carried out in order to determine the static structure factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$. Hence, from $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ we have obtained the pair-correlation functions, the ground-state energy which essentially is the correlation energy, the pressure of the gas, and, from Feynman's relation, the energy spectrum of elementary excitations. The response of the system to a static impurity charge has also been investigated. In the high-density limit our calculations show the same results as those given by Bogoliubov's perturbation theory. In the intermediate-density region, corresponding to the strongly coupled system, our results are in very good agreement with recent calculations based on the hypernetted-chain integral equation as well as Monte Carlo computations.
The parametrized form of local-field corrections is introduced to construct the dielectric function and the nonlocal spin susceptibility that describe the dielectric properties of a paramagnetic degenerate electron liquid in two dimensions beyond the random-phase approximation (RPA). The parameters that take into account the spin-parallel and spin-antiparallel electron-electron interactions at short distances are determined in such a way that the response functions correctly give the Monte Carlo values for the compressibility and the spin susceptibility, respectively, in the long-wavelength limit. The local-field correction thus obtained is compared with that in the Hubbard approximation; the static dielectric function and the spin susceptibility are also compared with those in the RPA. It is found that the sign of the static dielectric function depends on both the dimensionless coupling constant and the wave number, which is a feature markedly different from the RPA results.
We develop a finite-temperature field-theoretical description of the Casimir interaction between two perfectly conducting boundaries with the intervening gap filled by a two-component quantum Boltzmann plasma embedded in a homogeneous dielectric background. The quantum motion of the charged particles is represented by imaginary-time worldlines, while the electromagnetic field is treated in the Gaussian approximation. The resulting partition function contains distinct longitudinal and transverse response contributions and an additional quantum-induced source term with no classical counterpart. In the classical limit the theory reduces to the usual Casimir-screening picture: the static longitudinal mode is Debye screened, whereas the transverse electromagnetic sector is unaffected by classical mobile charges. Finite thermal de Broglie wavelengths modify the nonzero Matsubara response and produce the leading quantum correction to the force. In the static long-wavelength limit, the longitudinal dielectric function has, through the leading quantum correction, the same expansion structure as the Lindhard response of a degenerate electron gas under the correspondence kTF↔κDk_{TF}\leftrightarrowκ_DkTF​↔κD​ and kF↔λdB−1k_F\leftrightarrowλ_{dB}^{-1}kF​↔λdB−1​, while the static transverse response reproduces the leading high-temperature Landau orbital diamagnetic susceptibility.