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arXiv:cond-mat/9809008

Exactly solvable Kondo problem in the open $t-J$ chains

Jianhui Dai, Yupeng Wang

Published Sep 1, 1998• 0 citations
arXivHTMLPDF

Abstract

We study the problem of a boundary magnetic impurity coupled with the solvable $t-J$ chains. Our model provides a good start point to understand the Kondo problem in a Luttinger liquid as well as in a strongly correlated host. The Kondo coupling constant $J$ can take arbitrary values, which allows us to study the ferromagnetic and antiferromagnetic Kondo problems simultaneously. It is shown that both the Kondo coupling and the scalar potential effectively reconcile the spin dynamics at low temperatures. Generally, the impurity spin is split into two ghost spins via coupling effect. The residual entropy, which can be exactly derived for the present model, is strongly interaction-dependent. This hints the local spin configuration is very complicated and very different from that in the conventional Kondo problem. An unscreening phenomenon in the antiferromagnetic regime is found, which reveals the impurity potential plays an important role for the Kondo problem in a strongly correlated host. The low temperature specific heat is calculated in the framework of local Landau-Luttinger liquid theory.

DOI
10.48550/arxiv.cond-mat/9809008

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Exactly solvable Kondo problem in the open t−Jt-Jt−J chains
We study the problem of a boundary magnetic impurity coupled with the solvable t−Jt-Jt−J chains. Our model provides a good start point to understand the Kondo problem in a Luttinger liquid as well as in a strongly correlated host. The Kondo coupling constant JJJ can take arbitrary values, which allows us to study the ferromagnetic and antiferromagnetic Kondo problems simultaneously. It is shown that both the Kondo coupling and the scalar potential effectively reconcile the spin dynamics at low temperatures. Generally, the impurity spin is split into two ghost spins via coupling effect. The residual entropy, which can be exactly derived for the present model, is strongly interaction-dependent. This hints the local spin configuration is very complicated and very different from that in the conventional Kondo problem. An unscreening phenomenon in the antiferromagnetic regime is found, which reveals the impurity potential plays an important role for the Kondo problem in a strongly correlated host. The low temperature specific heat is calculated in the framework of local Landau-Luttinger liquid theory.
We study the problem of a boundary magnetic impurity coupled with the solvable $t\ensuremath{-}J$ chain. This model provides a good starting point to understand the Kondo problem in a Luttinger liquid as well as in a strongly correlated host. As the Kondo coupling constant Ji{J}_{i}Ji​ may take arbitrary values without breaking the integrability, we can study the ferromagnetic and antiferromagnetic Kondo problems simultaneously. It is shown that the boundary coupling generally splits the impurity spin into two effective spins and induces the interaction-dependent residual entropy. The absence of Kondo screening in an antiferromagnetic Kondo coupling regime is found, which indicates a genuine competing effect between the Kondo coupling Ji{J}_{i}Ji​ and the impurity potential Vi.{V}_{i}.Vi​. A local Landau-Luttinger liquid description is proposed to calculate the specific heat of the impurity.
To study the impurity potential effect to the Kondo problem in a Luttinger liquid, we propose an integrable model of two interacting half-chains coupled with a single magnetic impurity ferromagnetically. It is shown that the scalar potential effectively reconciles the spin dynamics at low temperatures. Generally, there is a competition between the Kondo coupling J and the impurity potential V. When the ferromagnetic Kondo coupling dominates over the impurity potential (V<∣SJ∣),(V<|\mathrm{SJ}|),(V<∣SJ∣), the Furusaki-Nagaosa many-body singlet can be perfectly realized. However, when the impurity potential dominates over the Kondo coupling (V> ∣SJ∣),(V>~|\mathrm{SJ}|),(V> ∣SJ∣), the fixed point predicted by Furusaki and Nagaosa is unstable and the system must flow to a weak-coupling fixed point. It is also found that the effective moment of the impurity measured from the susceptibility is considerably enlarged by the impurity potential. In addition, some quantum phase transitions driven by the impurity potential are found and the anomaly residual entropy is discussed.
To study the impurity potential effect to the Kondo problem in a Luttinger liquid, we introduce a model of ferromagnetic single-impurity Kondo problem in a multi-band one-dimensional δ-potential Fermi gas, which is exactly solvable for a special Kondo coupling constant via Bethe ansatz. It is found that the boundary potential modifies the local moment seriously due to the charge-spin coupling and the strong backward scattering off the impurity, and thus strongly affects the fixed point of the system. Generally, their is a residual entropy for the ground state which depends on the strength of the boundary potential. In addition, the tunneling effect through the impurity and the breakdown of the open boundary induced by the impurity are also discussed.
In this paper, the Kondo magnetic effect is studied for the XXZ\mathrm{XXZ}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.
We propose an integrable Kondo problem in a one-dimensional $t\ensuremath{-}J$ model. With the open boundary condition of the wave functions at the impurity sites, the model can be exactly solved via Bethe ansatz for a set of JL,R{J}_{L,R}JL,R​ (Kondo coupling constants) and VL,R{V}_{L,R}VL,R​ (impurity potentials) parametrized by a single parameter ccc. The integrable value of JL,R{J}_{L,R}JL,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.
We propose an integrable model of the spin-1/2 Heisenberg chain coupled to two impurity moments. With the open boundary conditions at the impurity sites, the model can be exactly solved for arbitrary impurity spin and arbitrary exchange constants between the bulk and the impurities. The absence of redundant terms in the Hamiltonian makes the model very reasonable. The Hamiltonian is diagonalized via algebraic Bethe ansatz. It is found that the impurity spins can only be screened (partially for S>1/2S>1/2S>1/2) for antiferromagnetic coupling between the impurity and the bulk. Otherwise the impurity spins cannot be screened. The residual entropy of the ground state and the Kondo temperature are also derived explicitly based on the Bethe ansatz and the local Fermi-liquid theory.