Showing papers on "Luttinger parameter published in 2012"
TL;DR: In this article, a microscopic derivation of the two-particle inelastic backscattering process in the presence of a time-reversal invariant Rashba impurity potential is presented.
Abstract: The occurrence of two-particle inelastic backscattering has been conjectured in helical edge states of topological insulators and is expected to alter transport. Here, by using a renormalization group approach, we provide a microscopic derivation of this process, in the presence of a time-reversal invariant Rashba impurity potential. We are able to prove that such an effect only occurs in the presence of electron-electron interactions. Furthermore, we find that the linear conductance as a function of temperature exhibits a crossover between two scaling behaviors, ${T}^{4K}$ for $Kg1/2$ and ${T}^{8K\ensuremath{-}2}$ for $Kl1/2$, with $K$ the Luttinger parameter.
67 citations
TL;DR: In this article, the authors revisited the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and showed 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.
Abstract: 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 regime of strong electron-electron interactions on the edge and strong Kondo coupling. We apply similar methods to the problem of a regular one-dimensional array of quantum impurities interacting with the edge liquid. When the edge electrons are at half-filling with respect to the impurity lattice, the system remains gapless unless the Luttinger parameter of the edge is less than $1/2$ in which case two-particle backscattering effects drive the system to a gapped phase with long-range Ising antiferromagnetic order. This is in marked contrast with the gapped disordered ground state of the ordinary half-filled one-dimensional Kondo lattice.
39 citations
TL;DR: In this article, the authors developed a method to extract the universal conductance of junctions of multiple quantum wires, a property of systems connected to reservoirs, from static ground-state computations in closed finite systems.
Abstract: We develop a method to extract the universal conductance of junctions of multiple quantum wires, a property of systems connected to reservoirs, from static ground-state computations in closed finite systems. The method is based on a key relationship, derived within the framework of boundary conformal field theory, between the conductance tensor and certain ground-state correlation functions. Our results provide a systematic way of studying quantum transport in the presence of strong electron-electron interactions using efficient numerical techniques such as the standard time-independent density-matrix renormalization-group method. We give a step-by-step recipe for applying the method and present several tests and benchmarks. As an application of the method, we calculate the conductance of the M fixed point of a Y junction of Luttinger liquids for several values of the Luttinger parameter $g$ and conjecture its functional dependence on $g$.
28 citations
TL;DR: In this paper, the conductance of stable fixed points of two and three quantum wires with different Luttinger parameters was evaluated within the framework of boundary conformal field theory, and the numerical results showed very good agreement with the analytical predictions.
Abstract: Within the framework of boundary conformal field theory, we evaluate the conductance of stable fixed points of junctions of two and three quantum wires with different Luttinger parameters. For two wires, the physical properties are governed by a single effective Luttinger parameter for each of the charge and spin sectors. We present numerical density-matrix-renormalization-group calculations of the conductance of a junction of two chains of interacting spinless fermions with different interaction strengths, obtained using a recently developed method [ Phys. Rev. Lett. 105 226803 (2010)]. The numerical results show very good agreement with the analytical predictions. For three spinless wires (i.e., a Y junction) we analytically determine the full phase diagram and compute all fixed-point conductances as a function of the three Luttinger parameters.
27 citations
TL;DR: In this article, the gap behavior as a function of the cylinder radius is analyzed and the Luttinger exponent remains non-trivial in the Tao-Thouless limit as well as for simple truncated states that can be constructed on the cylinder.
Abstract: We study fractional quantum Hall states in the cylinder geometry with open boundaries. We focus on principal fermionic 1/3 and bosonic 1/2 fractions in the case of hard-core interactions. The gap behavior as a function of the cylinder radius is analyzed. By adding enough orbitals to allow for edge modes we show that it is possible to measure the Luttinger parameter of the non-chiral liquid formed by the combination of the two counterpropagating edges when we add a small confining potential. While we measure a Luttinger exponent consistent with the chiral Luttinger theory prediction for the full hard-core interaction, the exponent remains non-trivial in the Tao-Thouless limit as well as for simple truncated states that can be constructed on the cylinder. If the radius of the cylinder is taken to infinity the problem becomes a Tonks-Girardeau one-dimensional interacting gas in Fermi and Bose cases. Finally we show that the the Tao-Thouless and truncated states have an edge electron propagator which decays spatially with a Fermi-liquid exponent even if the energy spectrum can still be described by a non-trivial Luttinger parameter.
7 citations
TL;DR: In this paper, the authors investigated the quantum phase transition between the one-channel Kondo (1CK) and 2CK fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators (2DTI) with Luttinger parameter.
Abstract: We investigate theoretically the quantum phase transition (QPT) between the one-channel Kondo (1CK) and two-channel Kondo (2CK) fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators (2DTI) with Luttinger parameter $0 1 that the 2CK fixed point can be unstable towards the 1CK fixed point and the system may undergo a quantum phase transition between 1CK and 2CK fixed points. The QPT in our model comes as a result of the combined Kondo and the helical Luttinger physics in 2DTI, and it serves as the first example of the 1CK-2CK QPT that is accessible by the controlled RG approach. We extract quantum critical and crossover behaviors from various thermodynamical quantities near the transition. Our results are robust against particle-hole asymmetry for 1/2
3 citations