Comparative study of theoretical methods for non-equilibrium quantum transport

Eckel, J.; Heidrich-Meisner, Fabian; Jakobs, Severin G.; Thorwart, Michael; Pletyukhov, Mikhail; Egger, Reinhold

doi:10.1088/1367-2630/12/4/043042

Cited by 129 publications

(167 citation statements)

References 96 publications

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“…[46][47][48][49] The Gutzwiller approximation has been generalized to the time-dependent case 50 and so has numerical renormalization group (NRG) [51][52][53][54] where however some issues with the use of Wilson chains in nonequilibrium systems have been pointed out by Rosch. 55 Dual-fermion approaches 56 have been proposed as well as superoperator techniques. 57,58 Some recent work attempts to compare several of these theories [59][60][61] and shed light on the critical issue of time scales involved. 62 Finally, some results for the SIAM are available 63 from numerically exact time evolution by a combination of density matrix renormalization group (DMRG) 64 and successive time evolution via time-dependent DMRG (tDMRG).…”

Section: Published By the American Physical Society Under The Terms Omentioning

confidence: 99%

Steady-state spectra, current, and stability diagram of a quantum dot: A nonequilibrium variational cluster approach

et al. 2012

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We calculate steady-state properties of a strongly correlated quantum dot under voltage bias by means of nonequilibrium cluster perturbation theory and the nonequilibrium variational cluster approach, respectively. Results for the steady-state current are benchmarked against data from accurate matrix product state based time evolution. We show that for low to medium interaction strength, nonequilibrium cluster perturbation theory already yields good results, while for higher interaction strength the self-consistent feedback of the nonequilibrium variational cluster approach significantly enhances the accuracy. We report the current-voltage characteristics for different interaction strengths. Furthermore we investigate the nonequilibrium local density of states of the quantum dot and illustrate that within the variational approach a linear splitting and broadening of the Kondo resonance is predicted which depends on interaction strength. Calculations with applied gate voltage, away from particle-hole symmetry, reveal that the maximum current is reached at the crossover from the Kondo regime to the doubly occupied or empty quantum dot. Obtained stability diagrams compare very well to recent experimental data [A. V. Kretinin et al., Phys. Rev. B 84, 245316 (2011)].

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Section: Published By the American Physical Society Under The Terms Omentioning

confidence: 99%

Steady-state spectra, current, and stability diagram of a quantum dot: A nonequilibrium variational cluster approach

et al. 2012

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“…The former are based on either a mean-field approximation or perturbative schemes, where the inclusion of higher order corrections is not always clear or systematic, and thus may lead to questionable results. Numerical brute-force approaches, such as time-dependent numerical renormalization-group techniques [12][13][14][15] , iterative [16][17][18] or stochastic [19][20][21][22] diagrammatic methods, and wave function based approaches 23 , have been very fruitful, but are limited in the range of parameters and timescales that can be studied.…”

Section: Introductionmentioning

confidence: 99%

Bistability in a nonequilibrium quantum system with electron-phonon interactions

et al. 2013

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The existence of more than one steady-state in a many-body quantum system driven out-ofequilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this paper, we combine a reduced density matrix formalism with the multilayer multiconfiguration time-dependent Hartree method to address this problem. This allows us to obtain a converged numerical solution of the nonequilibrium dynamics. Considering a generic model for quantum transport through a quantum dot with electron-phonon interaction, we prove that a unique steady-state exists regardless of the initial electronic preparation of the quantum dot, consistent with the converged numerical results. However, a bistability can be observed for different initial phonon preparations. The effects of the phonon frequency and strength of the electron-phonon couplings on the nonequilibrium dynamics and on the emergence of bistability is discussed.

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“…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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Comparative study of theoretical methods for non-equilibrium quantum transport

Cited by 129 publications

References 96 publications

Steady-state spectra, current, and stability diagram of a quantum dot: A nonequilibrium variational cluster approach

Steady-state spectra, current, and stability diagram of a quantum dot: A nonequilibrium variational cluster approach

Bistability in a nonequilibrium quantum system with electron-phonon interactions

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

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