This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges. It is shown that the scattering theory for waves in two dimensions, due to Buchholz, is still valid under these weaker assumptions. The concepts of interaction and asymptotic completeness, provided by this theory, are adopted in the present investigation.

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We study the formation of molecular states in a two-electron quantum dot as a function of the barrier potential dividing the dot. The increasing barrier potential drives the two electron system from an artificial helium atom to an artificial hydrogen molecule. To study this strongly coupled regime, we introduce variational wavefunctions which describe accurately two electrons in a single dot, and then study their mixing induced by the barrier. The evolution of the singlet-triplet gap with the barrier potential and with an external magnetic field is analyzed.