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Exact Friedel oscillations in the g=1/2 Luttinger liquid

A. Leclair·F. Lesage·H. Saleur
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Abstract

A single impurity in the 1D Luttinger model creates a local modification of the charge density analogous to the Friedel oscillations. In this paper, we present an exact solution of the case $g={1\over 2}$ (the equivalent of the Toulouse point) at any temperature $T$ and impurity coupling, expressing the charge density in terms of a hypergeometric function. We find in particular that at $T=0$, the oscillatory part of the density goes as $\ln x$ at small distance and $x^{-1/2}$ at large distance.

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A. Leclair, F. Lesage, H. Saleur. 1996-06-19. Exact Friedel oscillations in the g=1/2 Luttinger liquid. https://doi.org/10.1103/physrevb.54.13597

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