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

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.

12 pages, 5 figures

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Cited by in corpus (25)

• The spin-incoherent Luttinger liquid
• Wigner crystal physics in quantum wires
• Exact wave functions of two-electron quantum rings
• Spin coupling in zigzag Wigner crystals
• Correlation effects in quasi one dimensional electron wires
• The electron lifetime in Luttinger liquids
• Uniform electron gases. I. Electrons on a ring
• Bosonization of strongly interacting electrons
• Absence of Wigner molecules in one-dimensional few-fermion systems with short-range interactions
• Exchange Coupling in a One-Dimensional Wigner Crystal
• Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires
• Scanned gate microscopy of a one-dimensional quantum dot
• Phase diagram of a quantum Coulomb wire
• Interacting electrons on a quantum ring: exact and variational approach
• Scattering of charge and spin excitations and equilibration of a one-dimensional Wigner crystal
• Robustness of Helical Edge States Under Edge Reconstruction
• Symmetry-broken local-density approximation for one-dimensional systems
• Multiple crossovers in interacting quantum wires
• Singular responses of spin-incoherent Luttinger liquids
• Spin-orbit coupling in quasi-one-dimensional Wigner crystals
• Junctions of Spin-Incoherent Luttinger Liquids with Ferromagnets and Superconductors
• Fermions with long and finite range interactions on a quantum ring
• Matrix product states and first quantization
• The exchange coupling of a Wigner dimer
• Symmetry breaking and restoration on a fermionic quantum ring