Liu, DE; Zheng, H; Finkelstein, G; Baranger, HU, *Tunable quantum phase transitions in a resonant level coupled to two dissipative baths*,
Physical Review B, vol. 89 no. 8
(February, 2014),
pp. 085116 [PhysRevB.89.085116], [doi] .
**Abstract:**

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