Exact Friedel oscillations in theg=1/2 Luttinger liquid

A single impurity in the one-dimensional 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=1/2 (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 lnx at small distance and ${\mathit{x}}^{\mathrm{-}1/2}$ at large distance. © 1996 The American Physical Society.