Observing a bath induced phase transition via entropy detection in quantum dots*

Entropy measurements based on charge detection are becoming a powerful probe of mesoscopic systems. It is thus of great practical interest to study the backaction of the detector, typically a quantum point contact (QPC), in such experiments. In this work, we demonstrate the possibility that the measured entropy is strongly influenced by the backaction of the detector. More precisely, we show the detector could act as a bath and induce a dissipative quantum phase transition, in which the entropy of the total system is sharply modified across the transition point. We construct a simple and yet  general theory for such phase transition, and most importantly, we show the backaction of the QPC detector is encoded in one single parameter, the phase shift, which can be directly read out from the conductance. Using numerical renormalization group (NRG) we predict the system's phase diagram at finite temperature and finite coupling. This serves as a guide of experiments to observe  bath induced quantum phase transitions through entropy measurements, and thus understand the role of the charge detector as an integral part of the system.