Real-time simulations of nonequilibrium transport in the single-impurity Anderson model

Heidrich-Meisner, Fabian; Feiguin, Adrian; Dagotto, Elbio

doi:10.1103/physrevb.79.235336

Cited by 182 publications

(253 citation statements)

References 54 publications

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“…In earlier work 31 we have found that the 2B approximation is in excellent agreement with accurate TD-DMRG results in the regime of weak to intermediate interaction strength for the Anderson impurity model. 35 Hence the 2B approximation is extremely useful for benchmarking other approximations. The main quantity of MBPT is the Keldysh Green's function, G(z,z ), where z and z are time coordinates on the Keldysh contour C. [47][48][49] To describe the electron dynamics of the system, the Keldysh Green's function is propagated in time according to the KB equations.…”

Section: Many-body Technique: Kadanoff-baym Equationsmentioning

confidence: 99%

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Correlation effects in bistability at the nanoscale: Steady state and beyond

et al. 2012

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The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the nonequilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born, and GW level. Assuming the existence of a steady state and solving directly the steady-state equations we find multiple solutions in the HF approximation and within the ALDA. In these cases we investigate whether and how these solutions can be reached through time evolution and how to reversibly switch between them. We further show that for the same cases the inclusion of dynamical correlation effects suppresses bistability.

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Section: Many-body Technique: Kadanoff-baym Equationsmentioning

confidence: 99%

“…The calculations are performed with the fully self-consistent second-Born (2B) and GW approximations which have recently been shown 31 to agree with numerically exact TD-DMRG results. 35 In all cases studied here where adiabatic DFT and HF theory predict bistability dynamical XC effects destroy the phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Correlation effects in bistability at the nanoscale: Steady state and beyond

et al. 2012

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“…79 Other efforts along the same direction include the numerical path integral approach, [80][81][82] real-time quantum Monte Carlo simulations, 83,84 the numerical renormalization group approach, 85 and the time-dependent density matrix renormalization group approach. 86 For a comparison and an overview of various different methods in the related problem of nonequilibrium transport with electron-electron interaction, see Ref. 87.…”

Section: Introductionmentioning

confidence: 99%

Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions

Wang

Pshenichnyuk

Härtle

et al. 2011

The Journal of Chemical Physics

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The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory within second quantization representation of the Fock space, a novel numerically exact methodology to treat manybody quantum dynamics for systems containing identical particles, is applied to study the effect of vibrational motion on electron transport in a generic model for single-molecule junctions. The results demonstrate the importance of electronic-vibrational coupling for the transport characteristics. For situations where the energy of the bridge state is located close to the Fermi energy, the simulations show the time-dependent formation of a polaron state that results in a pronounced suppression of the current corresponding to the phenomenon of phonon blockade. We show that this phenomenon cannot be explained solely by the polaron shift of the energy but requires methods that incorporate the dynamical effect of the vibrations on the transport. The accurate results obtained with the ML-MCTDH in this parameter regime are compared to results of nonequilibrium Green's function theory.

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“…Although most of these studies are restricted to the steady-state regime, more recently there has been increasing activity to describe the time evolution towards the steady state as the system is driven out of equilibrium by applying a bias in the leads. These studies use a range of methods such as, e.g., TDDFT [2,[17][18][19][20], generalized master equations [21], many-body perturbation theory [22][23][24], the timedependent density-matrix renormalization group [25][26][27], a quantum trajectory approach [28], or real-time path integral [29] and Monte Carlo approaches [30].…”

Section: Model Hamiltonian For Time-dependent Transportmentioning

confidence: 99%

Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport

Kurth

Stefanucci

2011

Chemical Physics

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The cornerstone of time-dependent (TD) density functional theory (DFT), the Runge-Gross theorem, proves a one-to-one correspondence between TD potentials and TD densities of continuum Hamiltonians. In all practical implementations, however, the basis set is discrete and the system is effectively described by a lattice Hamiltonian. We point out the difficulties of generalizing the Runge-Groos proof to the discrete case and thereby endorse the recently proposed TD bond-current functional theory (BCFT) as a viable alternative. TDBCFT is based on a one-to-one correspondence between TD Peierl's phases and TD bond-currents of lattice systems. We apply the TDBCFT formalism to electronic transport through a simple interacting device weakly coupled to two biased non-interacting leads. We employ Kohn-Sham Peierls phases which are discontinuous functions of the density, a crucial property to describe Coulomb blockade. As shown by explicit time propagations, the discontinuity may prevent the biased system from ever reaching a steady state.

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Real-time simulations of nonequilibrium transport in the single-impurity Anderson model

Cited by 182 publications

References 54 publications

Correlation effects in bistability at the nanoscale: Steady state and beyond

Correlation effects in bistability at the nanoscale: Steady state and beyond

Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions

Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport

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