Despite the ubiquity of quantum phase transitions (QPT) in contemporary theoretical physics, obtaining clear experimental signatures has been challenging. I start by presenting a recent experiment in which it was possible to thoroughly characterize a QPT caused by coupling to an environment. The system is a single-molecule transistor built from a carbon nanotube quantum dot connected to strongly dissipative contacts. The electrical conductance of this system is highly singular at low temperature : the conductance is 0 except at one special point (on resonance and symmetric coupling) at which electrons are fully transmitted with unit probability— this is the quantum critical point.
I then turn to the theoretical understanding of this QPT obtained by mapping the problem onto that of a resonant Majorana fermion level in an interacting electron liquid. The unitary transmission obtained in the experiment is seen as a competition between the two leads, as in the two-channel Kondo problem. The deviations from unitarity at nonzero temperature are connected to residual interactions among the Majoranas.
Finally, I present theoretical results for tunneling through two quantum dots in the Kondo regime, a system which potentially has an interesting intermediate fixed point (that of the two-impurity Kondo model). While the normal tendency of dissipation is to destroy interesting many-body correlations, we show that in this case coupling to the bath stabilizes the intermediate fixed point and renders it experimentally observable.