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Physical Review Letters

Magnetic Impurity in an Open Correlated Electron Chain

Andrei A. Zvyagin

Published Dec 8, 1997• 29 citations
Publisher

Abstract

The exact solution of an integrable model with a magnetic (hybridization) impurity located at the edge of an open correlated electron chain is presented. It is argued that in the case when the impurity is connected to the host via a ``weak link'' its low-energy behavior coincides with that of an impurity in a periodic chain. The effects from impurities and boundary potentials are analyzed and compared.

DOI
10.1103/physrevlett.79.4641

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The Hubbard chain with a magnetic impurity of arbitrary spin SSS is studied using the Bethe ansatz technique. We consider two kinds of impurities which interact with itinerant electrons on the neighboring lattice sites without destroying the integrability. The correlations in the host always induce valence fluctuations at the impurity site. For a repulsive Hubbard UUU, an impurity coupled via antiferromagnetic exchange to the host reveals magnetic properties similar to those of the ordinary Kondo effect. In contrast, a hybridization impurity (Anderson-like) embedded into the attractive Hubbard model gives rise to essentially different magnetic behavior. This difference is a consequence of the spin gap in the host.
We consider an integrable model describing an Anderson-like impurity coupled to an open ttt-JJJ chain. Both the hybridization (i.e., its coupling to bulk chain) and the local spectrum can be controlled without breaking the integrability of the model. As the hybridization is varied, holon and spinon bound states appear in the many body ground state. Based on the exact solution we study the state of the impurity and its contribution to thermodynamic quantities as a function of an applied magnetic field. Kondo behavior in the magnetic response of the impurity can be observed provided that its parameters have been adjusted properly to the energy scales of the holon and spinon excitations of the one-dimensional bulk.
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.