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Exchange interaction in quantum rings and wires in the Wigner-crystal limit

Michael M. Fogler·Eugene Pivovarov
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Abstract

We present a controlled method for computing the exchange coupling in correlated one-dimensional electron systems based on the relation between the exchange constant and the pair-correlation function of spinless electrons. This relation is valid in several independent asymptotic regimes, including low electron density case, under the general condition of a strong spin-charge separation. Explicit formulas for the exchange constant are obtained for thin quantum rings and wires with realistic Coulomb interactions by calculating the pair-correlation function via a many-body instanton approach. A remarkably smooth interpolation between high and low electron density results is shown to be possible. These results are applicable to the case of one-dimensional wires of intermediate width as well. Our method can be easily generalized to other interaction laws, such as the inverse distance squared one of the Calogero-Sutherland-Moser model. We demonstrate excellent agreement with the known exact results for the latter model and show that they are relevant for a realistic experimental setup in which the bare Coulomb interaction is screened by an edge of a two-dimensional electron gas.

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Michael M. Fogler, Eugene Pivovarov. 2005-10-11. Exchange interaction in quantum rings and wires in the Wigner-crystal limit. https://doi.org/10.1103/physrevb.72.195344

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