Exact finite-size spectrum for the multi-channel Kondo model and Kac-Moody fusion rules

The finite-size spectrum for the multi-channel Kondo model is derived analytically from the exact solution, by mapping the nontrivial Z$_{n}$ part of the Kondo scattering into that for the RSOS model coupled with the impurity. The analysis is performed for the case of $n-2S=1$, where $n$ is the number of channel and $S$ is the impurity spin. The result obtained is in accordance with the Kac-Moody fusion hypothesis proposed by Affleck and Ludwig.Comment: RevTex, 4 page

Hyperelliptic curves for multi-channel quantum wires and the multi-channel Kondo problem

We study the current in a multi-channel quantum wire and the magnetization in the multi-channel Kondo problem. We show that at zero temperature they can be written simply in terms of contour integrals over a (two-dimensional) hyperelliptic curve. This allows one to easily demonstrate the existence of weak-coupling to strong-coupling dualities. In the Kondo problem, the curve is the same for under- and over-screened cases; the only change is in the contour.Comment: 7 pages, 1 figure, revte

On The Multichannel Kondo Model"

A detailed and comprehensive study of the one-impurity multichannel Kondo model is presented. In the limit of a large number of conduction electron channels $k \gg 1$, the low energy fixed point is accessible to a renormalization group improved perturbative expansion in $1/k$. This straightforward approach enables us to examine the scaling, thermodynamics and dynamical response functions in great detail and make clear the following features: i) the criticality of the fixed point; ii) the universal non-integer degeneracy; iii) that the compensating spin cloud has the spatial extent of the order of one lattice spacing.Comment: 28 pages, REVTEX 2.0. Submitted to J. Phys.: Cond. Mat. Reference .bbl file is appended at the end. 5 figures in postscript files can be obtained at [email protected]. The filename is gan.figures.tar.z and it's compressed. You can uncompress it by using commands: "uncompress gan.figures.tar.z" and "tar xvf gan.figures.tar". UBC Preprin

Theoretical analysis of the transmission phase shift of a quantum dot in the presence of Kondo correlations

We study the effects of Kondo correlations on the transmission phase shift of a quantum dot coupled to two leads in comparison with the experimental determinations made by Aharonov-Bohm (AB) quantum interferometry. We propose here a theoretical interpretation of these results based on scattering theory combined with Bethe ansatz calculations. We show that there is a factor of 2 difference between the phase of the S-matrix responsible for the shift in the AB oscillations, and the one controlling the conductance. Quantitative agreement is obtained with experimental results for two different values of the coupling to the leads.Comment: 4 pages, 4 figures, accepted for publication in Physical Review Letter

Kinks in the Kondo problem

We find the exact quasiparticle spectrum for the continuum Kondo problem of $k$ species of electrons coupled to an impurity of spin $S$. In this description, the impurity becomes an immobile quasiparticle sitting on the boundary. The particles are ``kinks'', which can be thought of as field configurations interpolating between adjacent wells of a potential with $k+1$ degenerate minima. For the overscreened case $k>2S$, the boundary has this kink structure as well, which explains the non-integer number of boundary states previously observed. Using simple arguments along with the consistency requirements of an integrable theory, we find the exact elastic $S$-matrix for the quasiparticles scattering among themselves and off of the boundary. This allows the calculation of the exact free energy, which agrees with the known Bethe ansatz solution.Comment: 9 pages +1 figur

Finite-temperature properties of the two-orbital Anderson model

The metallic phase of the two-orbital Anderson lattice is study in the limit of infinite spatial dimensions, where a second order perturbation treatment is used to solve the single-site problem. Using this approximation, in the Kondo regime, we find that the finite temperature properties of the conduction electrons exhibit the same behaviour as observed in the metallic phase of the two-channel Kondo lattice. Possible connections between these two models are discussed.Comment: 4 pages, 2 figures, to appear in Journal of Physics: Condensed Matte

Finite temperature bosonization

Finite temperature properties of a non-Fermi liquid system is one of the most challenging probelms in current understanding of strongly correlated electron systems. The paradigmatic arena for studying non-Fermi liquids is in one dimension, where the concept of a Luttinger liquid has arisen. The existence of a critical point at zero temperature in one dimensional systems, and the fact that experiments are all undertaken at finite temperature, implies a need for these one dimensional systems to be examined at finite temperature. Accordingly, we extended the well-known bosonization method of one dimensional electron systems to finite temperatures. We have used this new bosonization method to calculate finite temperature asymptotic correlation functions for linear fermions, the Tomonaga-Luttinger model, and the Hubbard model.Comment: REVTex, 48 page

Localization Length in Anderson Insulator with Kondo Impurities

The localization length, $\xi$, in a 2--dimensional Anderson insulator depends on the electron spin scattering rate by magnetic impurities, $\tau_s^{-1}$. For antiferromagnetic sign of the exchange, %constant, the time $\tau_s$ is {\em itself a function of $\xi$}, due to the Kondo correlations. We demonstrate that the unitary regime of localization is impossible when the concentration of magnetic impurities, $n_{\tiny M}$, is smaller than a critical value, $n_c$. For $n_{\tiny M}>n_c$, the dependence of $\xi$ on the dimensionless conductance, $g$, is {\em reentrant}, crossing over to unitary, and back to orthogonal behavior upon increasing $g$. Sensitivity of Kondo correlations to a weak {\em parallel} magnetic field results in a giant parallel magnetoresistance.Comment: 5 pages, 1 figur

Lattice path integral approach to the one-dimensional Kondo model

An integrable Anderson-like impurity model in a correlated host is derived from a gl(2$|$1)-symmetric transfer matrix by means of the Quantum-Inverse-Scattering-Method (QISM). Using the Quantum Transfer Matrix technique, free energy contributions of both the bulk and the impurity are calculated exactly. As a special case, the limit of a localized moment in a free bulk (Kondo limit) is performed in the Hamiltonian and in the free energy. In this case, high- and low-temperature scales are calculated with high accuracy.Comment: 26 pages, 9 figure

Kondo effect in two-dimensional disordered electron systems

We investigate the Kondo effect in two-dimensional disordered electron systems using a finite-temperature quantum Monte Carlo method. Depending on the position of a magnetic impurity, the local moment is screened or unscreened by the spin of the conduction electron. On the basis of the results, we show that the distribution of the Kondo temperature becomes wide and the weight at $T_K=0$ becomes large as randomness increases. The average susceptibility shows a weak power-law or logarithmic divergence at low temperature, indicating a non-Fermi-liquid behavior.Comment: 2 pages, 2 figures, to be published in supplement of J. Phys. Soc. Japan, Proceedings of Localisation 2002, (Tokyo, Japan, 2002