Real-time renormalization group and cutoff scales in nonequilibrium applied to an arbitrary quantum dot in the Coulomb blockade regime

Korb, Thomas; Reininghaus, Frank; Schoeller, Herbert; König, Jürgen

doi:10.1103/physrevb.76.165316

Cited by 40 publications

(51 citation statements)

References 27 publications

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“…realtime RG [17][18][19][20] or functional RG [21][22][23] either work far from the SC-FP or rely on an approximation to produce explicit results in the SC regime. Exact results, beside their fundamental interest, would therefore be a precious tool to assess the validity of more general, approximate methods.…”

Section: ∂I ∂V V=0mentioning

confidence: 99%

Out-of-Equilibrium Properties and Nonlinear Effects for Interacting Quantum Impurity Systems in the Strong-Coupling Regime

Freton

Boulat²

2014

Phys. Rev. Lett.

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We provide an exact description of out-of-equilibrium fixed points in quantum impurity models, that is able to treat time-dependent forcing. Building on this, we then show that analytical out-ofequilibrium results, that exactly treat interactions, can be obtained in interacting quantum impurity models in their strong coupling regime, provided they are integrable at equilibrium and they are "super Fermi liquids", i.e. they only allow for integer charge hopping. For such systems we build an out-of-equilibrium strong coupling expansion, akin to a Sommerfeld expansion in interacting systems. We apply our approach to the Interacting Resonant Level model, and obtain the exact expansion around the low energy fixed point of the universal scaling function for the charge current as a function of voltage, temperature, and frequency, up to order seven.The study of nano structures forced out-of-equilibrium is a vivid field of research, driven amongst other things by long term efforts towards the miniaturization of electronics. Rapid progresses in the realization of engineered micrometric structures coupled to macroscopic electrodes (e.g. quantum dots [1, 2]), or of hybrid devices consisting of atoms or molecules embedded in circuits [3][4][5] demonstrate the possibility of "single electron" electronics [6, 7]. A theoretical understanding of the mechanisms governing transport in those systems is thus of crucial importance. Whereas linear response -when the voltage across the nanostructure goes to zero -boils down to equilibrium properties and is fairly well understood, nonlinear effects are significantly harder to predict: solving the out-of-equilibrium theory unfortunately turns out to be a considerable problem, mixing many-body aspects (interactions make it complicated) with the intrinsically open geometry of the out-of-equilibrium problem.Those systems are modeled by quantum impurity models (QIM), that consist in continua of electronic degrees of freedom representing the metallic electrodes (the baths) interacting with the nanostructure (the "impurity"). A generic feature of QIM at equilibrium is that the impurity/bath coupling, no matter how small, has drastic consequence on the groundstate of the system: impurity degrees of freedom hybridize with the bath, so that effectively some, or all, impurity degrees of freedom are swallowed by the baths. In the zero energy E → 0 (groundstate) limit, impurity degrees of freedom are strongly bound to the baths, so that is is often called a strong coupling (SC) fixed point (FP). This last term means that the system has scale invariance in this limit [8, 9], resulting in the fact that the SC-FP is essentially an homogenous (the impurity "disappears") and free theory. This has direct physical consequences: for example, for systems with a Fermi liquid SC-FP [10,11], hybridization results in a linear I(V ) characteristic at small voltage, with the conductivity G 0 = ∂I ∂V V=0being maximal at T = 0 and at the particle-hole symmetric point. A typical energy scale, called here the hybridiza...

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Section: ∂I ∂V V=0mentioning

confidence: 99%

Out-of-Equilibrium Properties and Nonlinear Effects for Interacting Quantum Impurity Systems in the Strong-Coupling Regime

Freton

Boulat²

2014

Phys. Rev. Lett.

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“…If they were still present during a process of continuous renormalization, this would lead to divergences whenever the zero eigenvalue of L would appear in the resolvent (z − X − L) −1 (see also Ref. 55). The verticesG must therefore be integrated out before any continuous RG can be formulated.…”

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confidence: 99%

Fermionic superoperators for zero-temperature nonlinear transport: Real-time perturbation theory and renormalization group for Anderson quantum dots

2012

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We study electron quantum transport through a strongly interacting Anderson quantum dot at finite bias voltage and magnetic field at zero temperature using the real-time renormalization group (RT-RG) in the framework of a kinetic (generalized master) equation for the reduced density operator. To this end, we further develop the general, finite-temperature real-time transport formalism by introducing field superoperators that obey fermionic statistics. This direct second quantization in Liouville Fock space strongly simplifies the construction of operators and superoperators that transform irreducibly under the Anderson-model symmetry transformations. The fermionic field superoperators naturally arise from the univalence (fermion-parity) superselection rule of quantum mechanics for the total system of quantum dot plus reservoirs. Expressed in these field superoperators, the causal structure of the perturbation theory for the effective time-evolution superoperator kernel becomes explicit. Using the constraints of the causal structure, we construct a parametrization of the exact effective time-evolution kernel for which we analytically find the eigenvectors and eigenvalues in terms of a minimal set of only 30 independent coefficients. The causal structure also implies the existence of a fermion-parity protected eigenvector of the exact Liouvillian, explaining a recently reported result on adiabatic driving [Contreras-Pulido et al., Phys. Rev. B 85, 075301 (2012)] and generalizing it to arbitrary order in the tunnel coupling . Furthermore, in the wide-band limit, the causal representation exponentially reduces the number of diagrams for the time-evolution kernel. The remaining diagrams can be identified simply by their topology and are manifestly independent of the energy cutoff term by term. By an exact reformulation of this series, we integrate out all infinite-temperature effects, obtaining an expansion targeting only the nontrivial, finite-temperature corrections, and the exactly conserved transport current follows directly from the time-evolution kernel. From this new series, the previously formulated RT-RG equations are obtained naturally. We perform a complete one-plus-two-loop RG analysis at finite voltage and magnetic field, while systematically accounting for the dependence of all renormalized quantities on both the quantum dot and reservoir frequencies. Using the second quantization in Liouville space and symmetry restrictions, we obtain analytical RT-RG equations, which can be solved numerically in an efficient way, and we extensively study the model parameter space, excluding the Kondo regime where the one-plus-two-loop approach is obviously invalid. The incorporated renormalization effects result in an enhancement of the inelastic cotunneling peak, even at a voltage ∼magnetic field ∼tunnel coupling . Moreover, we find a tunnel-induced nonlinearity of the stability diagrams (Coulomb diamonds) at finite voltage, both in the single-electron tunneling and inelastic cotunneling regime.

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“…However, even more useful information can be found in the finite-frequency (FF) current noise, which can be used to probe the crossover between different quantum statistics of the quasiparticles. Recently, there has been theoretical studies on the FF current noise of a non-equilibrium Kondo dot [67][68][69] . So far, these studies have not been extended to the non-equilibrium FF current noise of a dissipative quantum dot.…”

Section: Non-equilibrium Finite-frequency Current Noisementioning

confidence: 99%

Nonequilibrium quantum transport through a dissipative resonant level

Chung¹,

Hur

Finkelstein

et al. 2013

Phys. Rev. B

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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 non-equilibrium 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 non-equilibrium current in the presence of a finite bias voltage V . In the linear response regime V → 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 non-equilibrium 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 non-equilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for V < T , while it obeys a distinct non-equilibrium profile for V > T . We furthermore provide new 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 non-equilibrium 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 488, 61, (2012).

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Real-time renormalization group and cutoff scales in nonequilibrium applied to an arbitrary quantum dot in the Coulomb blockade regime

Cited by 40 publications

References 27 publications

Out-of-Equilibrium Properties and Nonlinear Effects for Interacting Quantum Impurity Systems in the Strong-Coupling Regime

Out-of-Equilibrium Properties and Nonlinear Effects for Interacting Quantum Impurity Systems in the Strong-Coupling Regime

Fermionic superoperators for zero-temperature nonlinear transport: Real-time perturbation theory and renormalization group for Anderson quantum dots

Nonequilibrium quantum transport through a dissipative resonant level

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