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Physical review. B, Condensed matter

Static dielectric response of charged bosons

Gayle A. Sugiyama, C. Bowen, B. J. Alder

Published Nov 15, 1992• 38 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.46.13042

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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.
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.
Using a Jastrow trial wave function and the hypernetted-chain integral equation, as well as Monte Carlo computations, to calculate energy expectation values, we have obtained a variational upper bound to the ground-state energy of the charged Bose gas over an extensive range of densities. In the high-density region our data are in good agreement with previous weak-coupling results. In the low-density (strong-coupling) limit, comparison of our fluid energies with the self-consistent phonon calculations of Glyde and Keech in the solid allow us to locate the Wigner transition for charged bosons at rs=139{r}_{s}=139rs​=139, where rs{r}_{s}rs​ is the usual density parameter. We propose a simple and accurate equation of state based on our numerical data. Furthermore, we find that the Bose condensate fraction drops from a value of about 80% at rs=2{r}_{s}=2rs​=2, to a small but finite value (\ensuremath{\sim}1%) at crystallization. Finally we use our results for the charged Bose gas to derive a heuristic equation of state of the electron gas in the strong-coupling limit (${r}_{s}\ensuremath{\gg}1$).
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.
We study the two-dimensional gas of charged bosons interacting via a logarithmic potential within the quantal hypernetted-chain approximation. The pair correlation function, the static structure factor, the ground-state energy, and the spectrum of collective excitations are calculated over a range of the density parameter rs.{r}_{s}.rs​. We find that the static and dynamical properties are described rather well in this approach in comparison to previous theories. Our results are in good agreement with the available quantum Monte Carlo simulations.
Quantum Monte Carlo methods are used to calculate various ground-state properties of charged bosons in two dimensions, throughout the whole density range where the fluid phase is stable. Wigner crystallization is predicted at ${r}_{s}\ensuremath{\simeq}60.$ Results for the ground-state energy and the momentum distribution are summarized in analytic interpolation formulas embodying known asymptotic behaviors. Near freezing, the condensate fraction is less than 1%. The static structure factor S(k)S(k)S(k) and susceptibility $\ensuremath{\chi}(k)$ are obtained from the density-density correlation function in imaginary time, $F(\mathbf{k},\ensuremath{\tau}).$ An estimate of the energy of elementary excitations, given in terms of an upper bound involving S(k)S(k)S(k) and $\ensuremath{\chi}(k),$ is compared with the result obtained via analytic continuation from $F(\mathbf{k},\ensuremath{\tau}).$