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Physical review. B, Condensed matter

Correlation effects in the quasi-one-dimensional charged Bose condensate

Alfred Gold, L. Calmels

Published May 15, 1998• 3 citations
Publisher

Abstract

We describe correlation effects in the charged quasi-one-dimensional Bose condensate with parabolic confinement. Many-body effects are calculated with the sum-rule version of the Singwi, Tosi, Land, and Sj\"olander theory. We give numerical and analytical results for the local-field correction, the pair-distribution function, the correlation energy, and the compressibility of the Bose condensate. The results are given as a function of the Wigner-Seitz parameter ${r}_{s}$ and the wire-width parameter $b.$ The exact long-wavelength behavior of the plasmon dispersion is investigated using the compressibility sum rule.

DOI
10.1103/physrevb.57.12119

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We describe correlation effects in the charged quasi-one-dimensional Bose condensate with parabolic confinement. Many-body effects are calculated with the sum-rule version of the Singwi, Tosi, Land, and Sj"olander theory. We give numerical and analytical results for the local-field correction, the pair-distribution function, the correlation energy, and the compressibility of the Bose condensate. The results are given as a function of the Wigner-Seitz parameter rs{r}_{s}rs​ and the wire-width parameter b.b.b. The exact long-wavelength behavior of the plasmon dispersion is investigated using the compressibility sum rule.
We investigate the effect of many-body correlations on the ground-state properties of two coupled charged Bose quantum wires. The intrawire and interwire correlations are treated on the same footing within the self-consistent mean-field theory of Singwi, Tosi, Land and Sjölander. Static properties, viz. , pair-correlation functions, local-field correction factors, screened interactions and susceptibilities, are calculated for a range of wire spacings d , wire radii , and boson density parameters . We find that the qualitative dependence of intrawire correlations on and remains the same as found for an isolated wire, except that they become slightly weaker with the decreasing spacing d . The interwire correlations, on the other hand, depend strongly on d and are found to grow in magnitude with decreasing d . Further, we find no evidence for the existence of a charge-density-wave ground state in the density range investigated, , in the close proximity of wires. A comparison with the similar studies on the coupled electron quantum wires reveals that the charge-density-wave instability observed there may be an artifact of the neglect of interwire correlation effects.
In a recent paper we studied the ground-state energy of a quasi-one dimensional charged Bose condensate confined by a two-dimensional oscillator potential [l]. Many-body effects beyond the RPA have been taken into account by the local-field correction. In the present paper we study a quasi-one dimensional charged Bose condensate with a cylindrical confinement model (hard walls) and compare with the results of an electron gas. The following quantities are calculated : interaction energy, pair-correlation function, local-field correction, dielectric function, collective modes.
We evaluate the ground-state properties of a charged Bose gas at T=0T=0T=0 within the quantum version of the self-consistent field approximation of Singwi, Tosi, Land, and Sj\"olander. The dynamical nature of the local- field correction is retained to include dynamic correlation effects. The resulting static structure factor S(q)S(q)S(q) and the local-field factor G(q)G(q)G(q) exhibit properties not described by other mean-field theories.
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.
In this paper, we study correlations in quasi-one-dimensional electron systems. To account for the short-range correlations we have used a ladder approximation (LA), and to account for the long-range correlations we have used the Singwi, Tosi, S\"olander, and Land (STLS) scheme. After solving the integral equation appearing in the LA and solving the set of self-consistent equations of the STLS scheme, we join the resulting static structure factor in the large- and small-qqq limit smoothly. We then calculate the pair-correlation functions, the ground-state energy, the screened potential, and the plasmon dispersion relation. Our pair-correlation function remains positive everywhere (for rs< 6.5{r}_{s}<~6.5rs​< 6.5) and its value at the origin, g(0),g(0),g(0), is compared with the results of other calculational schemes. The screened potential is repulsive for rs< 2{r}_{s}<~2rs​< 2 and shows a weak attractive part for rs>2.{r}_{s}>2.rs​>2. We have argued that in these systems the sss-wave intrinsic superconductivity is absent. Finally, the quantities calculated in this paper are compared with the results of other calculational schemes.
We calculate the ground-state energy of a quasi-one-dimensional electron gas with Coulomb interaction depending on the spin-polarization parameter and the Wigner-Seitz parameter . Cylindrical quantum wires of radius are considered. We describe the pair-correlation function g(z = 0) as a function of and . We derive the spin-susceptibility as a function of and in different approximations. Numerical results obtained for the spin-susceptibility are fitted by an analytical expression. Collective modes (charge-density and spin-density excitations) in cylindrical quantum wires are described and the validity range of our calculation is discussed.