VOLUME 87, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 22 OCTOBER 2001

Kang and Cho Reply: The preceding Comment [1] ar-gues that the variational approximation scheme adopted inour Letter [2] is not appropriate to describe the Kondo limitof a coupled quantum-dot (QD)–Aharonov-Bohm (AB)ring system. The argument is based on earlier related Betheansatz results obtained by the author and his collaborator[3]. In spite of the discussions in Ref. [1], it should benoted that the model of Ref. [2] has never been solved ex-actly in the Kondo limit of d ø TK . The discussion in[1] completely ignores the difference between the modelin [2] and the one in earlier literature [3], which is verycrucial in determining the characteristics of the system.

The system considered in the author’s previous papers(Ref. [3]) has essentially different geometry from the onein our Letter [2]. The difference can be clearly seen by con-sidering the “decoupled” situation of the “metallic” hostfrom the impurity. In Ref. [3], the model consists of an in-dependent ideal AB ring and a Kondo impurity (or Ander-son impurity) if the two subsystems are decoupled (J � 0for the Kondo model, G � 0 for the Anderson model). Thepersistent current (PC) circulates the ideal ring which isnot affected by the impurity. On the other hand, the modelconsidered in our Letter [2] describes a quantum dot (orAnderson impurity) that carries the PC only by tunnelingto the other —noninteracting—part of the AB ring. In thedecoupled situation, the system consists of a finite-sizedlinear chain and the impurity. The system does not carrythe PC at all in the decoupled limit. It is quite clear that thismodel is drastically different from the one in [3], which hasalready been well noticed in the literature [4–6].

In this respect, the model considered in the author’sprevious papers [3] is equivalent to that of a QD side-attached to an AB ring studied in [5,6]. (Note that theauthors in [3] have considered a simpler chiral model forthe ring, which provides a slightly different result.) For themodel of a side-attached QD to an ideal AB ring, the Betheansatz result [5] shows that the presence of the Kondoimpurity does not affect the PC at all in the continuumlimit (d ! 0). That is, the PC of the system is equivalentto what is expected in an ideal ring with the same size.This can be regarded as a signature of the separation of

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charge degrees of freedom (that is, PC) from spin ones,as the author himself states [1]. For the exactly samegeometry of a QD side-attached to an AB ring, it hasbeen shown [6] that the approximation scheme adoptedin Ref. [2] reproduces the exact Bethe ansatz result of [5]in the d ø TK limit. As in the Bethe ansatz solution, theresult in [6] shows that the Kondo effect itself does notinfluence the AB oscillation in the d�TK ! 0 limit [6].This apparently demonstrates that the exact Bethe ansatzresult is rather in support of the validity of the variationalapproximation, in contrast to suggestions of the precedingComment [1].

In conclusion, the preceding Comment does not seem toprovide relevant discussions on our Letter [2], because itis based on a different model configuration.

Kicheon KangBasic Research LaboratoryElectronics and Telecommunications Research InstituteTaejon 305-350, Korea

Sam Young ChoInstitute of Physics and Applied PhysicsYonsei UniversitySeoul 120-749, Korea

Received 3 May 2001; published 8 October 2001DOI: 10.1103/PhysRevLett.87.179705PACS numbers: 72.15.Qm, 73.23.Hk, 73.23.Ra

[1] A. A. Zvyagin, preceding Comment, Phys. Rev. Lett. 87,179704 (2001).

[2] K. Kang and S.-C. Shin, Phys. Rev. Lett. 85, 5619 (2000).[3] A. A. Zvyagin and T. V. Bandos, Low Temp. Phys. 20, 222

(1994); A. A. Zvyagin, Low Temp. Phys. 21, 349 (1995).[4] M. Büttiker and C. A. Stafford, Phys. Rev. Lett. 76, 495

(1996).[5] H.-P. Eckle, H. Johannesson, and C. A. Stafford, Phys. Rev.

Lett. 87, 016602 (2001).[6] S. Y. Cho, K. Kang, C. K. Kim, and C.-M. Ryu, Phys.

Rev. B 64, 033314 (2001).

© 2001 The American Physical Society 179705-1