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

The Friedel oscillations in the vicinity of a Friedel-Anderson (FA) impurity are investigated numerically. For an FA impurity in the local moment limit the normalized amplitude A({\xi}) is S-shaped, approximately zero at short distances, approaching two at large distances and crossing the value one at the characteristic length {\xi}_{1/2}. Surprisingly, the Friedel oscillations of a simple non-interacting Friedel impurity with a narrow resonance at the Fermi level show a very...

Friedel oscillations appear in density of Fermi gases due to Pauli exclusion principle and translational symmetry breaking nearby a defect or impurity. In confined Fermi gases, this symmetry breaking occurs also near to boundaries. Here, density oscillations of a degenerate and confined Fermi gas are considered and characterized. True nature of density oscillations are represented by analytical formulas for degenerate conditions. Analytical characterization is first done for ...

When non-magnetic impurity immerses in Fermi sea, a regular modulation of charge density around impurity will appear and such phenomena is called Friedel oscillation (FO). Although both Luttinger liquid and Landau Fermi liquid show such characteristic oscillation, FO in generic non-Fermi liquid (NFL) phase is still largely unknown. Here, we show that FO indeed exists in NFL state of an exactly solvable model, i.e. the Hatsugai-Kohmoto model which has been intensively explored...

A model of interacting one--dimensional fermions confined to a harmonic trap is proposed. The model is treated analytically to all orders of the coupling constant by a method analogous to that used for the Luttinger model. As a first application, the particle density is evaluated and the behavior of Friedel oscillations under the influence of interactions is studied. It is found that attractive interactions tend to suppress the Friedel oscillations while strong repulsive inte...

The weakly interacting helical Luttinger liquid, due to spin momentum locking, is characterized by extremely peculiar local observables: we show that the density-density correlation functions do not exhibit signatures of Friedel and Wigner oscillations, and that spin-spin correlation functions, which are strongly anisotropic, witness the formation of a planar spin wave. Moreover, we demonstrate that the most relevant scattering potentials involving a localized impurity are no...

The Luttinger Theorem, which relates the electron density to the volume of the Fermi surface in an itinerant electron system, is taken to be one of the essential features of a Fermi liquid. The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral $I_{\rm L}$, which is also the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electro...

The charge and spin patterns of a quantum dot embedded into a spin-orbit coupled quantum wire subject to a magnetic field are investigated. A Luttinger liquid theory is developed, taking into account open boundaries and finite magnetic field. In the quasi-helical regime, when spin-orbit effects dominate over the Zeeman interaction, peculiar states develop at the Fermi surface of the dot. Anomalous Friedel oscillations with twice the expected wavelength develop in the wavefunc...

The density matrix renormalization group method for ladders works much more efficiently with open boundary conditions. One consequence of these boundary conditions is groundstate charge density oscillations that often appear to be nearly constant in magnitude or to decay only slightly away from the boundaries. We analyse these using bosonization techniques, relating their detailed form to the correlation exponent and distinguishing boundary induced generalized Friedel oscilla...

We propose a new non-Fermi liquid ground state in one dimension that is not of the Luttinger type. It is the ground state of fermions interacting via a long range repulsive interaction in real space of the form $ V(x) = e^2/|x| $. We characterise it by computing the momentum distribution which is perfectly flat near the Fermi points signalling a radical departure from Luttinger liquid theory(and Fermi liquid theory). The dispersion of elementary excitations is found to be sub...

We report the exact calculation of the Fermi-edge singularity exponent for correlated electrons in one dimension (Luttinger liquid). Focusing on the special interaction parameter g=1/2, the asymptotic long-time behavior can be obtained using the Wiener-Hopf method. The result confirms the previous assumption of an open boundary fixed point. In addition, a dynamic k-channel Kondo impurity is studied via Abelian bosonization for k=2 and k=4. It is shown that the corresponding o...