Dynamic correlations of the Coulomb Luttinger liquid

Abstract

The dynamic density response function, form-factor, and spectral function of a Luttinger liquid with Coulomb electron-electron interaction are studied with the emphasis on the short-range electron correlations. The Coulomb interaction changes dramatically the density response function as compared to the case of the short-ranged interaction. The form of the density response function is smoothing with time, and the oscillatory structure appears. However, the spectral functions remain qualitatively the same. The dynamic form-factor contains the $\delta$-peak in the long-wave region, corresponding to one-boson excitations. Besides, the multi-boson-excitations band exists in the wave-number region near to $2k_F$. The dynamic form-factor diverges at the edges of this band, while the dielectric function goes to zero there, which indicates the appearance of a soft mode. We develop a method to analyze the asymptotics of the spectral functions near to the edges of the multi-boson-excitations band.

11 pages, 3 figures, submitted to PRB

Cited by in corpus (4)

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• Quantum quench dynamics of the Coulomb Luttinger model
• Recursive Method for the Density of States in One Dimension
• Comment on "Dynamic correlations of the spinless Coulomb Luttinger liquid [Phys. Rev. B {\bf 65}, 125109 (2002)]"