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Acta Physica Polonica A

Persistent Currents and Bethe Ansatz

Gediminas Kiršanskas, Algirdas Matulis

Published Feb 1, 2011• 1 citation
Publisher

Abstract

The system of two electrons interacting with a single impurity in 1D metallic ring is considered illustrating the applicability of the Bethe Ansatz.
DOI
10.12693/aphyspola.119.158

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We describe a "train" effect which may exist in small metallic and semiconductor rings and might be associated with the long-standing problem of the persistent current enhancement. The current is associated with the cooperative motion of N electrons constituing the N-electron "train". The train arises via an excitation or a backflow of spin waves or of interchannel charge density sound modes. The impurities and defects have a little effect on the "train" current. The reason is that the "train" current is associated with a small momentum transfer, which is much smaller than the momentum transfer of the free electron current equal to 2 pi/L. For an illustration of the "train" effect we have calculated the persistent current in the framework of the Bethe ansatz solutions for Hubbard model. The fractional M/N periodicities of the persistent current serve as an indication of the electron "train"
We consider an integrable model of a one-dimensional mesoscopic ring, with the conduction electrons coupled by a spin exchange to a magnetic impurity. A symmetry analysis based on a Bethe ansatz solution of the model reveals that the current is insensitive to the presence of the impurity. We argue that this is true for any integrable impurity-electron interaction, independent of the choice of physical parameters or couplings. We propose a simple physical picture of how the persistent current gets protected by integrability.