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.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.

arXiv:1310.4773Physical Review BFeb 18, 201421 citations

Dissipative quantum phase transitions

Philipp Werner

Jan 1, 20053 citations

Nonequilibrium occupation number and charge susceptibility of a resonance level close to a dissipative quantum phase transition

Chung‐Hou Chung, K. V. P. Latha

Based on the recent paper [Phys. Rev. Lett. 102, 216803 (2009)], we study the nonequilibrium occupation number ${n}_{d}$ and charge susceptibility $\ensuremath{\chi}$ of a resonance level close to dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a delocalized phase for weak dissipation and a localized phase for strong dissipation. The resonance level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. Within the nonequilibrium renormalization-group approach, we calculate nonequilibrium magnetization $M$ and spin susceptibility $\ensuremath{\chi}$ in the effective Kondo model, corresponding to $2{n}_{d}\ensuremath{-}1$ and $\ensuremath{\chi}$ of a resonance level, respectively. We demonstrate the smearing of the KT transition in the nonequilibrium magnetization $M$ as a function of the effective anisotropic Kondo couplings, in contrast to a perfect jump in $M$ at the transition in equilibrium. In the limit of large bias voltages, we find $M$ and $\ensuremath{\chi}$ at the KT transition and in the localized phase show deviations from the equilibrium Curie-law behavior. As the system gets deeper in the localized phase, both ${n}_{d}\ensuremath{-}1/2$ and $\ensuremath{\chi}$ decrease more rapidly to zero with increasing bias voltages.Based on the recent paper [Phys. Rev. Lett. 102, 216803 (2009)], we study the nonequilibrium occupation number ${n}_{d}$ and charge susceptibility $\ensuremath{\chi}$ of a resonance level close to dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a delocalized phase for weak dissipation and a localized phase for strong dissipation. The resonance level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. Within the nonequilibrium renormalization-group approach, we calculate nonequilibrium magnetization $M$ and spin susceptibility $\ensuremath{\chi}$ in the effective Kondo model, corresponding to $2{n}_{d}\ensuremath{-}1$ and $\ensuremath{\chi}$ of a resonance level, respectively. We demonstrate the smearing of the KT transition in the nonequilibrium magnetization $M$ as a function of the effective anisotropic Kondo couplings, in contrast to a perfect jump in $M$ at the transition in equilibrium. In the limit of large bias voltages, we find $M$ and $\ensuremath{\chi}$ at the KT transition and in the localized phase show deviations from the equilibrium Curie-law behavior. As the system gets deeper in the localized phase, both ${n}_{d}\ensuremath{-}1/2$ and $\ensuremath{\chi}$ decrease more rapidly to zero with increasing bias voltages.

arXiv:1002.4038Physical Review BAug 30, 20103 citations

Quantum phase transition in a resonant level coupled to interacting leads

Henok T. Mebrahtu, Ivan Valerievich Borzenets, Dong E. Liu +5 more

arXiv:1208.1988NatureJul 31, 201292 citations

Driven-Dissipative Quantum Phase Transitions

Oscar Viyuela, Jiasen Jin, Alberto Biella +3 more

Bulletin of the American Physical SocietyMar 8, 20190 citations

Based on the recent paper [Phys. Rev. Lett. 102, 216803 (2009)], we study the nonequilibrium occupation number

{n}_{d}

and charge susceptibility $\ensuremath{\chi}$ of a resonance level close to dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a delocalized phase for weak dissipation and a localized phase for strong dissipation. The resonance level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. Within the nonequilibrium renormalization-group approach, we calculate nonequilibrium magnetization

M

and spin susceptibility $\ensuremath{\chi}$ in the effective Kondo model, corresponding to $2{n}_{d}\ensuremath{-}1$ and $\ensuremath{\chi}$ of a resonance level, respectively. We demonstrate the smearing of the KT transition in the nonequilibrium magnetization

M

as a function of the effective anisotropic Kondo couplings, in contrast to a perfect jump in

M

at the transition in equilibrium. In the limit of large bias voltages, we find

M

and $\ensuremath{\chi}$ at the KT transition and in the localized phase show deviations from the equilibrium Curie-law behavior. As the system gets deeper in the localized phase, both ${n}_{d}\ensuremath{-}1/2$ and $\ensuremath{\chi}$ decrease more rapidly to zero with increasing bias voltages.