Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model

In a recent work [Phys. Rev. Lett. {\bf 108}, 136401 (2012)] we have addressed the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. We have found that the physics associated with this model is qualitatively different from the elastic impurity setup analyzed by Kane and Fisher, and from the inelastic scattering scenario studied by Furusaki and Matveev, thus proposing a new paradigmatic picture of Luttinger liquid ...

We investigate the indirect interaction between two isolated impurities in a Luttinger liquid described by a microscopic lattice model. To treat the electron-electron interaction U the functional renormalization group method is used. For comparison we also study the U=0 case. We find that for a wide range of impurity parameters the impurity interaction V_{12} as a function of their separation r oscillates with decaying amplitude between being attractive and repulsive. For hal...

We study numerically the universal conductance of Luttinger liquids wire with a single impurity via the Muti-scale Entanglement Renormalization Ansatz (MERA). The scale invariant MERA provides an efficient way to extract scaling operators and scaling dimensions for both the bulk and the boundary conformal field theories. By utilizing the key relationship between the conductance tensor and ground-state correlation function, the universal conductance can be evaluated within the...

Interactions between electrons in one-dimension are fully described at low energies by only a few parameters of the Tomonaga-Luttinger model which is based on linearisation of the spectrum. We consider a model of spinless fermions with a short range interaction via the Bethe-Ansatz technique and show that a Luttinger parameter emerges in an observable beyond the low energy limit. A distinct feature of the spectral function, the edge that marks the lowest possible excitation e...

We compute exactly the non-equilibrium DC noise in a Luttinger liquid with an impurity and an applied voltage. By generalizing Landauer transport theory for Fermi liquids to interacting, integrable systems, we relate this noise to the density fluctuations of quasiparticles. We then show how to compute these fluctuations using the Bethe ansatz. The non-trivial density correlations from the interactions result in a substantial part of the non-equilibrium noise. The final result...

Using bosonization and path integral methods, we study general low temperature behavior of non-magnetic and magnetic impurity scattering in Tomonaga-Luttinger liquid, and calculate electron Green function for a general backward scattering potential. We demonstrate that electron density of state near the impurity site is suppressed by the backward scattering, but it mainly remains invariant as far away from the impurity, and at zero temperature the electrons are completely ref...

We show that thermodynamics is insufficient to probe the nature of the low energy dynamics of quantum impurity models and a more subtle analysis based on scattering theory is required. Traditionally, quantum impurity models are classified into one of two categories: Fermi liquids and non-Fermi liquids, depending on the analytic properties of the various thermodynamic quntities. We show, however, that even when a quantum impurity model is a Fermi liquid (an incoming electron a...

We study a system consisting of a Luttinger liquid coupled to a quantum dot on the boundary. The Luttinger liquid is expressed in terms of fermions interacting via density-density coupling and the dot is modeled as an interacting resonant level on to which the bulk fermions can tunnel. We solve the Hamiltonian exactly and construct all eigenstates. We study both the zero and finite temperature properties of the system, in particular we compute the exact dot occupation as a fu...

A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left- and right-movers, yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling de...

In this tutorial notes we review a functional bosonization approach in the Keldysh technique to one-dimensional Luttinger liquid in the presence of an impurity.