Dielectric response of a one-dimensional electron gas

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Abstract
The dielectric response of a quasi-one-dimensional system of interacting electrons has been investigated. In the authors' model the particles move freely in one direction and are tightly bound in the transverse direction. Calculation of the Coulomb matrix elements leads to an effective one-dimensional electron-electron interaction nu (q) which is less singular for small q than the 1/q2 potential assumed by previous authors. As a result, the excitonic instability which they find even for a rigid positive background does not arise in their calculation. The calculations are based on the approximation of Singwi, Tosi, Land and Sjolander (1968). As expected in this approach, the pair correlation function at small distances remains positive over a much larger range of densities than that for which the compressibility sum rule is satisfied. The static dielectric function is negative around q=2kF, which suggests the possibility of charge ordering when the background is allowed to be polarisable. If nu (q) is replaced by a delta -function potential, a numerical calculation of the energy for the exact solution of Yang may be made. On comparison with the result obtained with the method of Singwi et al. it is found that the approximate scheme gives good correlation energies for high densities.