A Scaling Approach for Interacting Quantum Wires -a Possible Explanation for the 0.7 Anomalous Conductance

We consider a weakly interacting finite wire with short and long range interactions. The long range interactions enhance the $4k_{F}$ scattering and renormalize the wire to a strongly interacting limit. For large screening lengths, the renormalized charge stiffness Luttinger parameter $K_{eff.}$ decreases to $K_{eff.}< {1/2}$, giving rise to a Wigner crystal at T=0 with an anomalous conductance at finite temperatures. For short screening lengths, the renormalized Luttinger parameter $K_{eff.}$ is restricted to ${1/2}\leq K_{eff.}\leq 1$. As a result, at temperatures larger than the magnetic exchange energy we find an interacting metal which for $K_{eff.}\approx {1/2}$ is equivalent to the Hubbard $U\to\infty$ model, with the anomalous conductance $G\approx\frac{e^2}{h}$ .