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Physical review. B, Condensed matter

Ground state of a two-dimensional charged-boson system

Chung‐In Um, W. H. Kahng, Eui-Soon Yim, Thomas F. George

Published Jan 1, 1990• 16 citations
Publisher

Abstract

The ground state of a two-dimensional charged-boson system is investigated over the range of densities 1\ensuremath{\lesssim}${R}_{s}$\ensuremath{\lesssim}10 in the self-consistent-field approximation; ${R}_{s}$=(${a}_{0}^{2}$\ensuremath{\pi}\ensuremath{\rho}${)}^{\mathrm{\ensuremath{-}}1/2}$, where ${a}_{0}$ is the Bohr radius and \ensuremath{\rho} is the number density. Starting with numerical self-consistent calculations of the static structure factor, the elementary excitation, pair-correlation functions, pressure, and ground-state energy are evaluated. These results are compared with those of the two-dimensional and three-dimensional systems obtained from other methods. The ground-state energy is given as ${\mathit{E}}_{0=\mathrm{\ensuremath{-}}1.2918{\mathit{R}}_{\mathit{s}}}^{\mathrm{\ensuremath{-}}2/3}$+0.03, which improves that result from the ring-diagram approximation.

DOI
10.1103/physrevb.41.259

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The ground state of a two-dimensional charged-boson system is investigated over the range of densities 1\ensuremath{\lesssim}Rs{R}_{s}Rs​\ensuremath{\lesssim}10 in the self-consistent-field approximation; Rs{R}_{s}Rs​=(a02{a}_{0}^{2}a02​\ensuremath{\pi}\ensuremath{\rho})\ensuremath−1/2{)}^{\mathrm{\ensuremath{-}}1/2})\ensuremath−1/2, where a0{a}_{0}a0​ is the Bohr radius and \ensuremath{\rho} is the number density. Starting with numerical self-consistent calculations of the static structure factor, the elementary excitation, pair-correlation functions, pressure, and ground-state energy are evaluated. These results are compared with those of the two-dimensional and three-dimensional systems obtained from other methods. The ground-state energy is given as E0=\ensuremath−1.2918Rs\ensuremath−2/3{\mathit{E}}_{0=\mathrm{\ensuremath{-}}1.2918{\mathit{R}}_{\mathit{s}}}^{\mathrm{\ensuremath{-}}2/3}E0=\ensuremath−1.2918Rs​\ensuremath−2/3​+0.03, which improves that result from the ring-diagram approximation.
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.
We study many-body effects of a charged-boson system in terms of a dynamically self-consistent method. We calculate static structure factors, elementary excitation energies, pair correlation functions, and ground-state energies for various densities through the iterative calculation using two independent relations between the structure factor and the local-field correction, and compare with a similar method using the local-field correction of Singwi et al. We claim that our ground-state energies may be considered as lower bounds.
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 $F(\mathbf{k},\ensuremath{\tau}).$
The ground-state energy of a charged boson gas at high density is evaluated exactly to second order in the density expansion, making use of complete sums of one- and two-ring diagrams. The result agrees numerically with Feenberg's variational calculation of the energy, although the methods appear to be substantially different. The presence of logarithmic terms in the energy, which are absent in the exact result, is shown to be a result of truncation of the Hamiltonian in the pair approximation or of inadequacies of variational wave functions which omit interpair correlations.
The ground state of a double-layer charged Bose system is investigated beyond the random-phase approximation by including the many-body correlation effects. The correlations within the layer are accounted for within the self-consistent theory of Singwi, Tosi, Land, and Sj\"olander, while we have neglected the effect of interlayer correlations. The static susceptibility, the elementary excitation spectrum, and the static screened potentials are calculated and their dependence on the boson number density and the layer spacing is examined. Results are compared with the recent work of Tanatar and Das where correlations are not included. It is found that the inclusion of correlation effects combined with the interlayer interactions can significantly alter the nature of the ground state and, in particular, can favor an inhomogeneous charge-density-wave ground state. A comparison is also made in terms of screened potentials with the double-layer electron system that enables one to have a deeper insight into the role played by the exchange and Coulomb correlations separately.