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The Friedel oscillations caused due to an impurity located at one edge of adisordered interacting quantum wire are calculated numerically. The electrondensity in the system's ground state is determined using the DMRG method, andthe Friedel oscillations data is extracted using the density difference betweenthe case in which the wire is coupled to an impurity and the case where theimpurity is uncoupled. We show that the power law decay of the oscillationsoccurring for an interacting clean 1D samples described by Luttinger liquidtheory, is multiplied by an exponential decay term due to the disorder. Scalingof the average Friedel oscillations by this exponential term collapses thedisordered samples data on the clean results. We show that the length scalegoverning the exponential decay may be associated with the Andersonlocalization length and thus be used as a convenient way to determine thedependence of the localization length on disorder and interactions. Thelocalization length decreases as a function of the interaction strength, inaccordance with previous predictions.Comment: 7 pages, 7 figure

Friedel oscillations in disordered quantum wires: Influence of electron-electron interactions on the localization length