Sharp superconductor-insulator transition in short wires

Recent experiments on short MoGe nanowires show a sharp superconducting-insulating transition at the universal resistance RQ=h/(4e2), contrary to the expectation of a smooth temperature dependence of the resistance for such Josephson-like systems. We present a self-consistent renormalization-group treatment of interacting quantum phase slips in short superconducting wires, which reproduces this sharp universal transition. Our method should also apply to other systems in the sine-Gordon universality class, in the previously inaccessible intermediate-coupling regime.