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

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 $g=\frac{1}{2}$ (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 $\ln x$ at small distance and $x^{-1/2}$ at large distance.

1 reference added. 13 pages, harvmac

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• Boundary conditions changing operators in non conformal theories
• Entanglement entropy and boundary renormalization group flow - exact results in the Ising universality class
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• Screening of a Luttinger liquid wire by a scanning tunneling microscope tip: I. Spectral properties
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• On the effects of irrelevant boundary scaling operators
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• Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems
• Local Magnetization in the Boundary Ising Chain at Finite Temperature
• Friedel oscillations of Density of States in a one-dimensional Mott insulator and Incommensurate Charge Density Wave/Superconductor
• Scattering amplitudes in non-Fermi liquid systems
• Charge and spin density in the helical Luttinger liquid
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