Flux Period, Spin Gap, and Pairing in the One-Dimensional t-J-J' Model.

Using the factorization of the wave function in the t-J-J' model at small exchange couplings, we demonstrate the connection between the existence of a spin gap and an hc/2e flux periodicity of the ground state energy. We conjecture that all spin-gapped SU(2)-invariant Luttinger liquids have hc/2e flux periodicity, and that this is connected to the fact that a gapped spin-1/2 chain always breaks translational symmetry by doubling the unit cell.