Real-time green's functions in many body problems

Schmutz, M.

doi:10.1007/bf01323673

Cited by 136 publications

(97 citation statements)

References 18 publications

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“…The development of this Liouville-Fock-space approach is a central topic of this paper. Our approach differs from previous formulations [31][32][33][34] both by its construction and by the scope of its application. The most closely related is that of Prosen, 31 which was used to calculate steady states of quadratic effective Liouvillians.…”

Section: Introductionmentioning

confidence: 97%

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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Section: Introductionmentioning

confidence: 97%

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

2012

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“…We also establish the notation and terminology which are used throughout the paper. This section is partly based in the formalism of superoperators developed by Schmutz in the context of real-time Green's functions method 50 . Some aspects of the superoperator nonequilibrium Green's function theory with application to electron transport have been recently discussed by Harbola and Mukamel.…”

Section: Liouville Space and Superoperator Formalismmentioning

confidence: 99%

Super-fermion representation of quantum kinetic equations for the electron transport problem

Dzhioev

Kosov

2011

The Journal of Chemical Physics

142

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We discuss the use of super-fermion formalism to represent and solve quantum kinetic equations for the electron transport problem. Starting with the Lindblad master equation for the molecule connected to two metal electrodes, we convert the problem of finding the nonequilibrium steady state to the many-body problem with non-Hermitian Liouvillian in super-Fock space. We transform the Liouvillian to the normal ordered form, introduce nonequilibrium quasiparticles by a set of canonical nonunitary transformations and develop general many-body theory for the electron transport through the interacting region. The approach is applied to the electron transport through a single level. We consider a minimal basis hydrogen atom attached to two metal leads in Coulomb blockade regime (out of equilibrium Anderson model) within the nonequilibrium Hartree-Fock approximation as an example of the system with electron interaction. Our approach agrees with exact results given by the Landauer theory for the considered models.

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“…The derivation of the generalized quantum-distribution-function-transport equations combines the Liouvillian super Green's function technique [3] and the lattice Weyl-Wigner formulation of the quantum theory of solids [4]. A generating superfunctional is constructed which allows an algebraic and straightforward application of quantum-field-theoretical techniques in real time to derive coupled quantum-transport, condensate, and pair-wavefunction equations.…”

Section: A2 Generalized Quantum-distribution Transport Equationsmentioning

confidence: 99%

“…Therefore, a fully quantum mechanical treatment of quantum dynamics of finite open systems is appropriately described by the time evolution equations in ( p, q, E, t) phase-space. Indeed, one of the simplest implementations of this generalization occurs in the time-dependent analysis of the high-speed behavior of resonant tunneling devices which made use of the Wigner distribution function transport equation [3]. So far, this is the only approach which has been successful in analyzing high-speed quantum-device physics.…”

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confidence: 99%

Landauer counting argument, quantum distribution-function transport equations, and nonequilibrium quantum statistical physics

Buot

Rajagopal

1998

Superlattices and Microstructures

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Real-time green's functions in many body problems

Cited by 136 publications

References 18 publications

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

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

Super-fermion representation of quantum kinetic equations for the electron transport problem

Landauer counting argument, quantum distribution-function transport equations, and nonequilibrium quantum statistical physics

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