arXiv:cond-mat/9708076 · Physical review. B, Condensed matter

Exact results for a Kondo impurity with electronic correlations

You‐Quan Li, P.-A. Barès

Published Nov 1, 1997• 4 citations

Abstract

A one-dimensional model of a Kondo impurity with arbitrary spin in the presence of electronic correlations is solved exactly. The Bethe ansatz equations are obtained for the case of quadratic dispersion. The ground state is studied in the thermodynamic limit, and the magnetic susceptibility at zero temperature is calculated.

DOI: 10.1103/physrevb.56.r11384

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arXiv:cond-mat/9708076 · Physical review. B, Condensed matter

Exact results for a Kondo impurity with electronic correlations

You‐Quan Li, P.-A. Barès

Published Nov 1, 1997• 4 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.56.r11384

Related papers

The Kondo effect in spin chains

Nicolas Laflorencie, Erik Schwartz Sørensen, Ian K. Affleck

It is well known that the free electron Kondo problem can be described by a one-dimensional (1D) model because only the s-wave part of the electronic wavefunction is affected by the Kondo coupling. Moreover, since only the spin degrees of freedom are involved in the Kondo interaction, and due to spin–charge separation in 1D, the universal low energy long distance physics of the Kondo model also arises when a magnetic impurity is coupled to the end of a gapless antiferromagnetic J 1 –J 2 spin- chain, where J 1 ( J 2 ) is the (next) nearest neighbor coupling. Experimental realizations of such spin chain models are possible and, using various analytical and numerical techniques, we present a detailed and quantitative comparison between the usual free electron Kondo model and such spin chain versions of the Kondo problem. For the gapless J 1 –J 2 spin chain two cases are studied, with zero next nearest neighbor coupling, J 2 = 0, and with a critical second-neighbor coupling, J 2 = J 2 c . We first focus on the spin chain impurity model with a critical second-neighbor antiferromagnetic exchange where a bulk marginal coupling present in the spin chain model for J 2 < J 2 c vanishes . There, the usual Kondo physics is recovered in the spin chain model in the low energy regime (up to negligible corrections, dropping as powers of inverse length or energy). At J 2 c the spin chain model is not exactly solvable and we demonstrate the equivalence to the Kondo problem by comparing density matrix renormalization group calculations on the frustrated spin chain model with exact Bethe ansatz calculations of the electronic Kondo problem. We then analyze the nearest neighbor model ( J 2 = 0) where a new kind of Kondo effect occurs due to the presence of the bulk marginal coupling. This marginal coupling slightly alters the β function for the Kondo coupling, leading to a slower variation of the Kondo temperature, T K , with the bare Kondo coupling. In their exact Bethe ansatz solution of this spin chain impurity model ( J 2 = 0), Frahm and Zvyagin noted this relation as well as the connection to the Kondo problem. Here, by numerically solving the Bethe ansatz equations we provide further evidence for the connection to Kondo physics and in addition we present low temperature quantum Monte Carlo results for the impurity susceptibility that further support this connection.It is well known that the free electron Kondo problem can be described by a one-dimensional (1D) model because only the s-wave part of the electronic wavefunction is affected by the Kondo coupling. Moreover, since only the spin degrees of freedom are involved in the Kondo interaction, and due to spin–charge separation in 1D, the universal low energy long distance physics of the Kondo model also arises when a magnetic impurity is coupled to the end of a gapless antiferromagnetic J 1 –J 2 spin- chain, where J 1 ( J 2 ) is the (next) nearest neighbor coupling. Experimental realizations of such spin chain models are possible and, using various analytical and numerical techniques, we present a detailed and quantitative comparison between the usual free electron Kondo model and such spin chain versions of the Kondo problem. For the gapless J 1 –J 2 spin chain two cases are studied, with zero next nearest neighbor coupling, J 2 = 0, and with a critical second-neighbor coupling, J 2 = J 2 c . We first focus on the spin chain impurity model with a critical second-neighbor antiferromagnetic exchange where a bulk marginal coupling present in the spin chain model for J 2 < J 2 c vanishes . There, the usual Kondo physics is recovered in the spin chain model in the low energy regime (up to negligible corrections, dropping as powers of inverse length or energy). At J 2 c the spin chain model is not exactly solvable and we demonstrate the equivalence to the Kondo problem by comparing density matrix renormalization group calculations on the frustrated spin chain model with exact Bethe ansatz calculations of the electronic Kondo problem. We then analyze the nearest neighbor model ( J 2 = 0) where a new kind of Kondo effect occurs due to the presence of the bulk marginal coupling. This marginal coupling slightly alters the β function for the Kondo coupling, leading to a slower variation of the Kondo temperature, T K , with the bare Kondo coupling. In their exact Bethe ansatz solution of this spin chain impurity model ( J 2 = 0), Frahm and Zvyagin noted this relation as well as the connection to the Kondo problem. Here, by numerically solving the Bethe ansatz equations we provide further evidence for the connection to Kondo physics and in addition we present low temperature quantum Monte Carlo results for the impurity susceptibility that further support this connection.

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We study a one-dimensional n -channel highly correlated electron model (based on the supersymmetric t-J model) with a magnetic impurity of arbitrary spin S that can hybridize with up to one itinerant electron per channel. The model extends the multichannel Kondo problem to correlations in the host and to the mixed valence regime. The Bethe ansatz equations are derived and solved for the ground state and for low temperatures. We conclude that the critical non-Fermi-liquid (overscreened) behaviour cannot be reached for this interacting electron system. Possible applications of the model are discussed.We study a one-dimensional n -channel highly correlated electron model (based on the supersymmetric t-J model) with a magnetic impurity of arbitrary spin S that can hybridize with up to one itinerant electron per channel. The model extends the multichannel Kondo problem to correlations in the host and to the mixed valence regime. The Bethe ansatz equations are derived and solved for the ground state and for low temperatures. We conclude that the critical non-Fermi-liquid (overscreened) behaviour cannot be reached for this interacting electron system. Possible applications of the model are discussed.

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{J}_{L,R}

(Kondo coupling constants) and

{V}_{L,R}

(impurity potentials) parametrized by a single parameter

c

. The integrable value of

{J}_{L,R}

runs from negative infinity to positive infinity, which allows us to study both the ferromagnetic Kondo problem and the antiferromagnetic Kondo problem in a strongly correlated electron system. Generally, there is a residual entropy for the ground state, which indicates a typical non-Fermi liquid behavior.

O(\frac{1}{\mathrm{ln}\mathcal{D}})

terms (

\mathcal{D}

is the ultraviolet cutoff) are neglected. The Kondo model with arbitrary impurity magnetic moment ${\ensuremath{\mu}}_{0}$ is discussed using both perturbative and nonperturbative methods. It is found that in the infinite-cutoff limit, the impurity's contribution to thermodynamic quantities is independent of the electron's magnetic moment $\ensuremath{\mu}$, and so one can make use of the known results for $\ensuremath{\mu}={\ensuremath{\mu}}_{0}$.

In this paper, the Kondo magnetic effect is studied for the

\mathrm{XXZ}

spin chain where the impurities are coupled to the edges of the system. The Hamiltonian of our model can be constructed from the transfer matrix. It is exactly solvable and the exchange constants between the bulk and the boundary impurities are arbitrary. The finite-size corrections to the ground-state energy are obtained for the magnetic impurities and the boundary condition. The specific heat and the susceptibility contributed by the impurities are derived and the Kondo temperature is given explicitly by the use of the Luttinger-Fermi liquid picture and the Bethe ansatz method.