One-Dimensional Electron Liquid in an Antiferromagnetic Environment: Spin Gap from Magnetic Correlations

We study a one-dimensional electron liquid coupled by a weak spin-exchange interaction to an antiferromagnetic spin- $S$ ladder with $n$ legs. A perturbative renormalization group analysis in the semiclassical limit reveals the opening of a spin gap, driven by the local magnetic correlations on the ladder. The effect, which we argue is present for any gapful ladder or gapless ladder with $\mathrm{nS}\gg 1$, is enhanced by the repulsive interaction among the conduction electrons but is insensitive to the sign of the spin exchange interaction with the ladder. Possible implications for the striped phases of the cuprates are discussed.