Laboratoire de Physique Théorique
Toulouse - UMR 5152

This work aimed to study Heisenberg exchange coupling in a one-dimensional Wigner crystal. The coupling may be seen as arising from quantum tunneling of the relative coordinate of the two electrons underneath the separating potential barrier. In the first approximation, one may treat all the other electrons as frozen during the tunneling. But, of course, in fact they are not — and thus they do contribute to the tunneling amplitude. With Konstantin Matveev and Alexios Klironomos, we studied this contribution :

A. D. Klironomos, RR, and K. A. Matveev, Phys. Rev. B 72, 195343 (2005)

The following figure shows the imaginary-time trajectories of the two exchanging electrons (red and blue), and of their nearest four neighbors (gray) :