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arXiv:cond-mat/0210664 · Physical review. B, Condensed matter

Self-consistent scattering theory of the pair distribution function in charged Bose fluids

B. Davoudi, Reza Asgari, Marco Polini, M. P. Tosi

Published May 6, 2003• 5 citations
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Abstract

We use a density-functional theoretical approach to calculate the pair distribution function and the effective interactions in homogeneous fluids of spinless charged bosons. The scheme involves the self-consistent solution of a two-particle scattering problem with an effective scattering potential which embodies many-body effects and is adjusted to the compressibility sum rule. Numerical results are presented over an extensive range of density in both three and two dimensions.

DOI
10.1103/physrevb.67.172503

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We use a density-functional theoretical approach to calculate the pair distribution function and the effective interactions in homogeneous fluids of spinless charged bosons. The scheme involves the self-consistent solution of a two-particle scattering problem with an effective scattering potential which embodies many-body effects and is adjusted to the compressibility sum rule. Numerical results are presented over an extensive range of density in both three and two dimensions.
Ground-state properties of a two-dimensional fluid of bosons with repulsive dipole-dipole interactions are studied by means of the Euler-Lagrange hypernetted-chain approximation. We present a self-consistent semianalytical theory of the pair distribution function g(r)g(r)g(r) and ground-state energy of this system. Our approach is based on the solution of a zero-energy scattering Schr\"odinger equation for the ``pair amplitude'' g(r)\sqrt{g(r)}g(r)​ with an effective potential from Jastrow-Feenberg correlations. We find excellent agreement with quantum Monte Carlo results over a wide range of coupling strength, nearly up to the critical coupling for the liquid-to-crystal quantum phase transition. We also calculate the one-body density matrix and related quantities, such as the momentum distribution function and the condensate fraction.
The static-linear-response function $\ensuremath{\chi}(k)$ is derived for the quantum Bose fluid with the use of the hypernetted-chain approximation in the Jastrow theory. The pair-correlation function of the uniform system required as an input function is optimized within the same theory. The compressibility sum rule as well as the sequential and screening conditions are exactly fulfilled by construction. It is shown analytically that in the small-wavelength limit the leading correction in ${\ensuremath{\chi}}^{\ensuremath{-}1}(k)$ to the freeparticle kinetic energy is a constant 23TJFN\frac{2}{3}\frac{{T}_{\mathrm{JF}}}{N}32​NTJF​​, where TJF{T}_{\mathrm{JF}}TJF​ is the Jackson-Feenberg kinetic energy. We have also developed a reliable numerical method which is used in the calculation of the linear-response function of the charged-boson gas at metallic densities.
The thermodynamics of a homogeneous dilute Bose gas with an arbitrarily strong repulsion between particles is investigated on the basis of the exact relation connecting the pair correlation function with the in-medium pair wave functions and occupation numbers. It is shown that the effective-interaction scheme, which is reduced to the Bogoliubov model with the effective pairwise potential, is not acceptable for investigating the short-range particle correlations in a dilute strongly interacting Bose gas. In contrast to this scheme, our model is thermodynamically consistent and free of the ultraviolet divergences due to accurate treatment of the short-range boson correlations. An equation for the in-medium scattering amplitude is derived that makes it possible to find the in-medium renormalization for the pair wave functions at short boson separations. Low-density expansions for the main thermodynamic quantities are reinvestigated on the basis of this equation. In addition, the expansions are found for the interaction and kinetic energies per particle. It is demonstrated that for a many-boson system of hard spheres the interaction energy is equal to zero for any boson density. The exact relationship between the chemical potential and in-medium pair wave functions is also established.
Some properties of a two-dimensional charged Bose gas interacting with a ln(r) potential are investigated on the basis of a self-consistent-field formalism which includes the short-range correlations between bosons through a local-field correction depending on the pair correlation function. Numerical results for the static structure factor, pair correlation function, spectrum of elementary excitations, and the response of the system to a static impurity charge are presented. Our results show the same qualitative behavior as those of the three-dimensional analog but the correlation effects are somewhat more pronounced in two dimensions.
The low-density expansions for the energy, chemical potential, and condensate depletion of the homogeneous dilute dipolar Bose gas are obtained by regularizing the dipole-dipole interaction at long distances. It is shown that the leading term, proportional to the density, allows a simple physical interpretation and consistently describes the thermodynamic stability of the system. The long-range asymptotics are obtained analytically for the normal and anomalous one-particle correlation functions and the pair distribution function. We discuss the properties of the two-body scattering with zero relative momentum for the dipole-dipole interaction; in particular, we derive the asymptotics of the wave function and a correction to the scattering length for small values of the dipolar range. We show how the density expansions can be derived within the Bogoliubov model of weakly interacting particles without any divergence from the assumption of universality of the expansions at low densities.
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.