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

Tunable quantum phase transitions in a resonant level coupled to two dissipative baths

Dong E. Liu, Huaixiu Zheng, Gleb Finkelstein +1 more

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

Phase Transition due to Quantum Dissipation

Kenichi Aoki, Tamao Kobayashi

素粒子論研究Jan 1, 20120 citations

Nonequilibrium quantum transport through a dissipative resonant level

Chung‐Hou Chung, Karyn Le Hur, Gleb Finkelstein +2 more

The resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the nonequilibrium transport near a quantum phase transition in a spinless dissipative resonant-level model, extending earlier work [Phys. Rev. Lett 102, 216803 (2009)]. A detailed derivation of a rigorous mapping of our system onto an effective Kondo model is presented. A controlled energy-dependent renormalization-group approach is applied to compute the nonequilibrium current in the presence of a finite bias voltage $V$ . In the linear-response regime $V\ensuremath{\rightarrow}0$, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the nonequilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the nonequilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for $V<T$ , while it obeys a distinct nonequilibrium profile for $V>T$ . We furthermore provide different signatures of the transition in the finite-frequency current noise and ac conductance via a recently developed functional renormalization group (FRG) approach. The generalization of our analysis to nonequilibrium transport through a resonant level coupled to two chiral Luttinger liquid leads, generated by fractional quantum Hall edge states, is discussed. Our work on the dissipative resonant level has direct relevance to experiments on a quantum dot coupled to a resistive environment, such as H. Mebrahtu et al., [Nature (London) 488, 61 (2012)].The resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the nonequilibrium transport near a quantum phase transition in a spinless dissipative resonant-level model, extending earlier work [Phys. Rev. Lett 102, 216803 (2009)]. A detailed derivation of a rigorous mapping of our system onto an effective Kondo model is presented. A controlled energy-dependent renormalization-group approach is applied to compute the nonequilibrium current in the presence of a finite bias voltage $V$. In the linear-response regime $V\ensuremath{\rightarrow}0$, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the nonequilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the nonequilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for $V<T$, while it obeys a distinct nonequilibrium profile for $V>T$. We furthermore provide different signatures of the transition in the finite-frequency current noise and ac conductance via a recently developed functional renormalization group (FRG) approach. The generalization of our analysis to nonequilibrium transport through a resonant level coupled to two chiral Luttinger liquid leads, generated by fractional quantum Hall edge states, is discussed. Our work on the dissipative resonant level has direct relevance to experiments on a quantum dot coupled to a resistive environment, such as H. Mebrahtu et al., [Nature (London) 488, 61 (2012)].

arXiv:1211.3748Physical Review BJun 21, 201311 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.

V

. In the linear-response regime $V\ensuremath{\rightarrow}0$, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the nonequilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the nonequilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for

V<T

, while it obeys a distinct nonequilibrium profile for

V>T

. We furthermore provide different signatures of the transition in the finite-frequency current noise and ac conductance via a recently developed functional renormalization group (FRG) approach. The generalization of our analysis to nonequilibrium transport through a resonant level coupled to two chiral Luttinger liquid leads, generated by fractional quantum Hall edge states, is discussed. Our work on the dissipative resonant level has direct relevance to experiments on a quantum dot coupled to a resistive environment, such as H. Mebrahtu et al., [Nature (London) 488, 61 (2012)].