Dissipation-induced quantum phase transition in a quantum box

In a recent work, Le Hur has shown, using perturbative arguments, that dissipative coupling to gate electrodes may play an important role in a quantum box near its degeneracy point [ K. Le Hur Phys. Rev. Lett. 92 196804 (2004)]: While quantum fluctuations of the charge of the dot tend to round Coulomb blockade charging steps of the box, strong enough dissipation suppresses these fluctuations and leads to the reappearance of sharp charging steps. In the present paper, we study this quantum phase transition in detail using bosonization and the numerical renormalization group in the limit of vanishing level spacing and map out the phase diagram using these nonperturbative methods. We also discuss the properties of the renormalized lead-dot conductance in the vicinity of the phase transition and determine the scaling properties of the dynamically generated crossover scale analytically.