2005/10/11 by M. M. Fogler, Michael M. Fogler, Eugene Pivovarov · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Classical mechanics #Condensed matter physics #Constant (computer programming) #Correlation function (quantum field theory) #Coulomb #Coupling constant #Electron #Geometry #Interpolation (computer graphics) #Inverse #Limit (mathematics) #Mathematical analysis #Mathematics #Molecular Junctions and Nanostructures #Physics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Spin (aerodynamics) #Wigner crystal #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.72.195344
published as Phys. Rev. B 72, 195344 (2005) · 12 pages, 5 figures
arxiv created 2005/10/11 · openalex publication_date 2005/11/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 the 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.