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

We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling which was missed by previous poor man's scaling treatments. The combination of an exact solution at the so-called decoupling point and a renormalization group analysis \`a la Anderson-Yuval-Hamann allows us to access the regim...

In this work, analytical expressions for the Green function of a Luttinger liquid are derived with one and two mobile impurities (heavy particles) using a combination of bosonization and perturbative approaches. The calculations are done in the random phase approximation (RPA) limit using the powerful non-chiral bosonization technique (NCBT) which is nothing but the resummation of the most singular parts of the RPA terms of the Green function expanded out in powers of the for...

We improve the recently developed functional renormalization group (fRG) for impurities and boundaries in Luttinger liquids by including renormalization of the two-particle interaction, in addition to renormalization of the impurity potential. Explicit flow-equations are derived for spinless lattice fermions with nearest neighbor interaction at zero temperature, and a fast algorithm for solving these equations for very large systems is presented. We compute spectral propertie...

The single impurity problem in a spinful Tomonaga-Luttinger liquid is studied numerically using path-integral Monte Carlo methods. The advantage of our approach is that the system allows for extensive analyses of charge and spin conductance in the non-perturbative regime. By closely examining the behavior of conductances at low temperatures, in the presence of a finite backward scattering barrier due to the impurity, we identified four distinct phases characterized by either ...

A continuum of excitations in interacting one-dimensional systems is bounded from below by a spectral edge that marks the lowest possible excitation energy for a given momentum. We analyse short-range interactions between Fermi particles and between Bose particles (with and without spin) using Bethe-Ansatz techniques and find that the dispersions of the corresponding spectral edge modes are close to a parabola in all cases. Based on this emergent phenomenon we propose an empi...

A quantum Monte Carlo simulation method has been developed and applied to study the critical behavior of a single Kondo impurity in a Luttinger liquid. This numerically exact method has no finite-size limitations and allows to simulate the whole temperature range. Focusing on the impurity magnetic susceptibility, we determine the scaling functions, in particular for temperatures well below the Kondo temperature. In the absence of elastic potential scattering, we find Fermi-li...

We introduce an integrable impurity model in which both electrons and impurity have spin and flavour degrees of freedom. This model is a generalization of the multi-channel Kondo model and closely related with resonant tunneling through quantum dot. The Hamiltonian is exactly diagonalized by means of the Bethe ansatz.

We compare two fermionic renormalization group methods which have been used to investigate the electronic transport properties of one-dimensional metals with two-particle interaction (Luttinger liquids) and local inhomogeneities. The first one is a poor man's method setup to resum ``leading-log'' divergences of the effective transmission at the Fermi momentum. Generically the resulting equations can be solved analytically. The second approach is based on the functional renorm...

Simple intersections between one-dimensional channels can act as coherent beam splitters for non-interacting electrons. Here we examine how coherent splitting at such intersections is affected by inter-particle interactions, in the special case of an intersection of topological edge states. We derive an effective impurity model which represents the edge-state intersection within Luttinger liquid theory at low energy. For Luttinger K = 1 / 2 , we compute the exact time-depende...

Using a precise coset Ising-Bose representation, we show how backscattering of electrons off a magnetic impurity destabilizes the two-channel Kondo fixed point and drives the system to a new fixed point, in agreement with previous results. In addition, we verify the scaling proposed by Furusaki and Nagaosa and prove that the other possible critical fixed point, namely the local Fermi liquid class, is not completely universal when backscattering is included because the Wilson ...