The Anderson impurity model out-of-equilibrium: Assessing the accuracy of simulation techniques with an exact current-occupation relation

We study the interacting, symmetrically coupled single impurity Anderson model. By employing the nonequilibrium Green’s function formalism, we reach an exact relationship between the steady-state charge current flowing through the impurity (dot) and its occupation. We argue that the steady-state cur...

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Bibliographic Details
Published in:The Journal of chemical physics 2017-08, Vol.147 (5), p.054104-054104
Main Authors: Agarwalla, Bijay Kumar, Segal, Dvira
Format: Article
Language:English
Subjects:
Computer simulation
Electrons
Equilibrium flow
Impurities
Mathematical models
Model accuracy
Occupations
Physics
Steady state
Transport phenomena
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Summary:We study the interacting, symmetrically coupled single impurity Anderson model. By employing the nonequilibrium Green’s function formalism, we reach an exact relationship between the steady-state charge current flowing through the impurity (dot) and its occupation. We argue that the steady-state current-occupation relation can be used to assess the consistency of simulation techniques and identify spurious transport phenomena. We test this relation in two different model variants: First, we study the Anderson-Holstein model in the strong electron-vibration coupling limit using the polaronic quantum master equation method. We find that the current-occupation relation is violated numerically in standard calculations, with simulations bringing up incorrect transport effects. Using a numerical procedure, we resolve the problem efficiently. Second, we simulate the Anderson model with electron-electron interaction on the dot using a deterministic numerically exact time-evolution scheme. Here, we observe that the current-occupation relation is satisfied in the steady-state limit—even before results converge to the exact limit.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.4996562