June 17, 1996
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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August 25, 1996
We show how to analytically determine for $g\leq 1/2$ the "Friedel oscillations" of charge density by a single impurity in a 1D Luttinger liquid of spinless electrons.
April 4, 1996
We study the density disturbance of a correlated 1D electron liquid in the presence of a scatterer or a barrier. The 2k_F-periodic density profile away from the barrier (Friedel oscillation) is computed for arbitrary electron--electron interaction and arbitrary impurity strength. We find that in presence of correlations, the Friedel oscillation decays slower than predicted by Fermi liquid theory. In the case of a spinless Luttinger liquid characterized by an interaction const...
October 1, 2007
Charge density and magnetization density profiles of one-dimensional metals are investigated by two complementary many-body methods: numerically exact (Lanczos) diagonalization, and the Bethe-Ansatz local-density approximation with and without a simple self-interaction correction. Depending on the magnetization of the system, local approximations reproduce different Fourier components of the exact Friedel oscillations.
September 16, 1995
We study Friedel oscillations in one-dimensional electron liquid for arbitrary electron-electron interaction and arbitrary impurity strength. For Luttinger liquid leads, the Friedel oscillations decay as x^-g far away from the impurity, where g is the interaction constant. For a weak scatterer, a slower decay is found at intermediate distances from the impurity, with a crossover to the asymptotic x^-g law.
October 4, 2000
We introduce a path-integral approach that allows to compute charge density oscillations in a Luttinger liquid with impurities. We obtain an explicit expression for the envelope of Friedel oscillations in the presence of arbitrary electron-electron potentials. As examples, in order to illustrate the procedure, we show how to use our formula for contact and Coulomb potentials.
November 20, 2018
In this work, the four-point Green functions relevant to the study of Friedel oscillations are calculated for a Luttinger liquid with a cluster of impurities around an origin using the powerful Non chiral bosonization technique (NCBT). The two-point functions obtained using the same method are used to calculate the dynamical density of states (DDOS), which exhibits a power law in energy and closed analytical expressions for the DDOS exponent is calculated. These results inter...
February 3, 2008
We show that the long distance charge density oscillations in a metal induced by a weakly coupled spin-1/2 magnetic impurity exhibiting the Kondo effect are given, at zero temperature, by a universal function F(r/xi_K) where r is the distance from the impurity and xi_K, the Kondo screening cloud size =v_F/T_K, where v_F is the Fermi velocity and T_K is the Kondo temperature. F is given by a Fourier-like transform of the T-matrix. Analytic expressions for F(r/xi_K) are derived...
October 1, 2014
We numerically study Friedel Oscillations and screening effect around a single impurity in one- and two-dimensional interacting lattice electrons. The interaction between electrons is accounted for by using a momentum independent self-energy obeying the Luttinger theorem. It is observed in one-dimensional systems that the amplitude of oscillations is systematically damped with increasing the interaction while the period remains unchanged. The variation of screening charge wit...
June 17, 2019
We study the asymptotic decay of the Friedel density oscillations induced by an open boundary in a one-dimensional chain of lattice fermions with a short-range two-particle interaction. From Tomonaga-Luttinger liquid theory it is known that the decay follows a power law, with an interaction dependent exponent, which, for repulsive interactions, is larger than the noninteracting value $-1$. We first investigate if this behavior can be captured by many-body perturbation theory ...
March 20, 2008
We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (ohmic) bath . For non-zero dissipation $\eta$ the weak link is always a relevant perturbation which suppresses transport strongly. At zero temperature the current voltage relation of the link is $I\sim \exp(-E_0/eV)$ where $E_0\sim\eta/\kappa$ and $\kappa$ denotes the compressibility. At non-zero temperature $T$ the linear conductance is proportional to $...