We study the effect of Coulomb interactions on the conductance of a single-mode quantum wire connecting two bulk leads. When the density of electrons in the wire is very low, they arrange in a finite-length Wigner crystal. In this regime the electron spins form an antiferromagnetic Heisenberg chain with an exponentially small coupling $J$. An electric current in the wire perturbs the spin chain and gives rise to a temperature-dependent contribution of the spin subsystem to the resistance. At low temperature $T\ll J$ this effect is small, and the conductance of the wire remains close to $2e^2/h$. At $T\gg J$ the spin effect reduces the conductance to $e^2/h$.

• Received 3 July 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.106801