Abstract
We consider transport through quantum dots with two tunnelling paths. The presence of multiple paths gives rise to Fano resonances exhibiting Kondo-like physics. To study such quantum dots we employ a generalized Anderson model which we argue to be integrable via the Bethe ansatz. The exact solution exhibits non-perturbative behaviour in the tunnelling strengths of both paths, reflective of electron trajectories with non-trivial winding number. While integrability allows the characterization of transport properties exactly, we argue that the non-perturbative behaviour arises at a more basic level, that of two-particle quantum mechanics. We further support the argued non-analyticities through exact diagonalization studies of an equivalent lattice model.
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