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

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

1996-06-17

arxiv.org/abs/cond-mat/9606124v2

Phys. Rev. B54, (1996) 13597.

Physics

Condensed Matter

1 reference added. 13 pages, harvmac

Scientific paper

10.1103/PhysRevB.54.13597

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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