Charging of a quantum dot coupled to Luttinger liquid leads

Luttinger liquid behavior of one-dimensional correlated electron systems is characterized by power-law scaling of a variety of physical observables with exponents determined by a single interaction dependent parameter K. We suggest a setup to study Luttinger liquid behavior in quantum wires which allows to determine K from two independent measurements: resonant transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two measured values of K for a single probe would provide strong experimental evidence for the Luttinger liquid paradigm.Comment: 4 pages, 4 figures included, version accepted for publication in PR

Influence of the contacts on the conductance of interacting quantum wires

We investigate how the conductance G through a clean interacting quantum wire is affected by the presence of contacts and noninteracting leads. The contacts are defined by a vanishing two-particle interaction to the left and a finite repulsive interaction to the right or vice versa. No additional single-particle scattering terms (impurities) are added. We first use bosonization and the local Luttinger liquid picture and show that within this approach G is determined by the properties of the leads regardless of the details of the spatial variation of the Luttinger liquid parameters. This generalizes earlier results obtained for step-like variations. In particular, no single-particle backscattering is generated at the contacts. We then study a microscopic model applying the functional renormalization group and show that the spatial variation of the interaction produces single-particle backscattering, which in turn leads to a reduced conductance. We investigate how the smoothness of the contacts affects G and show that for decreasing energy scale its deviation from the unitary limit follows a power law with the same exponent as obtained for a system with a weak single-particle impurity placed in the contact region of the interacting wire and the leads.Comment: 10 page, 4 figures included, minor changes in the summary, version accepted for publication in PR

A junction of three quantum wires: restoring time-reversal symmetry by interaction

We investigate transport of correlated fermions through a junction of three one-dimensional quantum wires pierced by a magnetic flux. We determine the flow of the conductance as a function of a low-energy cutoff in the entire parameter space. For attractive interactions and generic flux the fixed point with maximal asymmetry of the conductance is the stable one, as conjectured recently. For repulsive interactions and arbitrary flux we find a line of stable fixed points with vanishing conductance as well as stable fixed points with symmetric conductance (4/9)(e^2/h).Comment: 5 pages, 3 figures, version accepted for publication in Phys. Rev. Let

Comment on "Canonical and Mircocanonical Calculations for Fermi Systems"

In the context of nuclear physics Pratt recently investigated noninteracting Fermi systems described by the microcanonical and canonical ensemble. As will be shown his discussion of the model of equally spaced levels contains a flaw and a statement which is at least confusing.Comment: Comment on S. Pratt, Phys. Rev. Lett. 84, 4255 (2000) and nucl-th/990505

Finite-temperature linear conductance from the Matsubara Green function without analytic continuation to the real axis

We illustrate how to calculate the finite-temperature linear-response conductance of quantum impurity models from the Matsubara Green function. A continued fraction expansion of the Fermi distribution is employed which was recently introduced by Ozaki [Phys. Rev. B 75, 035123 (2007)] and converges much faster than the usual Matsubara representation. We give a simplified derivation of Ozaki's idea using concepts from many-body condensed matter theory and present results for the rate of convergence. In case that the Green function of some model of interest is only known numerically, interpolating between Matsubara frequencies is much more stable than carrying out an analytic continuation to the real axis. We demonstrate this explicitly by considering an infinite tight-binding chain with a single site impurity as an exactly-solvable test system, showing that it is advantageous to calculate transport properties directly on the imaginary axis. The formalism is applied to the single impurity Anderson model, and the linear conductance at finite temperatures is calculated reliably at small to intermediate Coulomb interactions by virtue of the Matsubara functional renormalization group. Thus, this quantum many-body method combined with the continued fraction expansion of the Fermi function constitutes a promising tool to address more complex quantum dot geometries at finite temperatures.Comment: version accepted by Phys. Rev.

Indirect forces between impurities in one-dimensional quantum liquids

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 half-filling of the band and in a crossover regime between weak and strong impurities the interaction becomes purely attractive. For U=0 and independent of the impurity strength the amplitude of the interaction energy falls off as 1/r. For U>0 the decay for small separations and weak to intermediate impurities is governed by a U dependent exponent larger than -1, which crosses over to -1 for large r. The crossover scale depends on the impurity strength and U. We present simple pictures which explain our results in the limits of weak and strong impurities. We finally also consider attractive interactions U<0.Comment: 8 pages, 9 figures include

Comment on ``Bethe Ansatz Results for the 4f-Electron Spectra of a Degenerate Anderson Model ''

In a recent letter, Zvyagin calculates the density of states for 4f electrons coupled to a conduction band in the framework of the Bethe ansatz (BA) solution for the degenerate Anderson model. It is claimed that the results qualitatively disagree with the results obtained for the same model but using a variational approach. Even the high energy feature in the f-spectral function near the 4f-level energy ef, i.e. the ``normal'' ionization peak (NIP), is argued to be qualitatively different in the two approaches. In the following we point out that this is not the case.Comment: 1 page, RevTeX, no figur