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We study tunneling through a resonant level connected to two dissipativebosonic baths: one is the resistive environment of the source and drain leads,while the second comes from coupling to potential fluctuations on a resistivegate. We show that several quantum phase transitions (QPT) occur in such amodel, transitions which emulate those found in interacting systems such asLuttinger liquids or Kondo systems. We first use bosonization to map thisdissipative resonant level model to a resonant level in a Luttinger liquid, onewith, curiously, two interaction parameters. Drawing on methods for analyzingLuttinger liquids at both weak and strong coupling, we obtain the phasediagram. For strong dissipation, a Berezinsky-Kosterlitz-Thouless QPT separatesstrong-coupling and weak-coupling (charge localized) phases. In thesource-drain symmetric case, all relevant backscattering processes disappear atstrong coupling, leading to perfect transmission at zero temperature. In fact,a QPT occurs as a function of the coupling asymmetry or energy of the resonantlevel: the two phases are (i) the system is cut into two disconnected pieces(zero transmission), or (ii) the system is a single connected piece withperfect transmission, except for a disconnected fractional degree of freedom.The latter arises from the competition between the two fermionic leads (sourceand drain), as in the two-channel Kondo effect.

Tunable Quantum Phase Transitions in a Resonant Level Coupled to Two Dissipative Baths