One-dimensional electron gas interacting with a Heisenberg spin-1/2 chain

We analyze a model of a one-dimensional electron-gas interacting with an antiferromagnetic Heisenberg spin-1/2 chain via the spin-exchange interactions. Using a solution at a special limit, we characterize the gapless modes of the spin-gap fixed point at weak coupling J_K≪J_H,E_F. We show that the only gapless pairing mode with divergent susceptibility is a composite odd-parity/odd-frequency singlet-pairing order parameter, while the ordinary BCS even-parity singlet-pairing mode is incoherent. For two-leg ladder systems, we note that it is possible to have a range of doping where the chemical potential cuts only the antibonding band while the bonding band remains half filled. We propose that in such a state the two-leg ladder is effectively realizing the one-dimensional Kondo-Heisenberg model.