Fictitious flux confinement: Magnetic pairing in coupled spin chains or planes

The spinon and holon excitations of two-leg Heisenberg or lightly doped t-J ladders are shown to be bound in pairs by string confinement forces given approximately by the antiferromagnetic exchange energy across the rungs, F=J_⊥〈SᵢSⱼ〉_⊥/b. These forces originate from fictitious flux tubes associated with the half-Fermi statistics of the excitations. It is conjectured that similar confinement forces, determined by the antiferromagnetic exchange energy across the layers, are partially responsible for the spin gap and the pairing of charge carriers in multilayer CuO superconductors.