Real-time diagrammatic Monte Carlo for nonequilibrium quantum transport

We propose a numerically exact approach to nonequilibrium real-time dynamics that is applicable to quantum impurity models coupled to biased noninteracting leads, such as those relevant to quantum transport in nanoscale devices. The method is based on a diagrammatic Monte Carlo sampling of the real-time perturbation theory along the Keldysh contour. We benchmark the method on a noninteracting resonant-level model and, as a first nontrivial application, we study zero-temperature nonequilibrium transport through a vibrating molecule.

Figure 1

(Color online) Example of a configuration with $k=3$ segments, each starting at $t_i^s$ and ending at $t_i^e$, $i=1,2,3$. Here blue (dark gray)/red (gray) dots stands for annihilation/creation operators of the initially occupied level while red segments indicate how the vertices are connected by the hybridization functions ${\Delta }_{\mathcal{K}}\left(t^e,t^s\right)$ in the particular configuration shown. Arrows indicate time-ordering operation along the contour.

Figure 2

(Color online) Zero-temperature real-time dynamics for different bias values $eV$ of the dot population, $⟨n\left(t\right)⟩$, from an initially occupied dot (left panel) and of the current, $⟨I\left(t\right)⟩$ (right panel) of the resonant-level model. DiagMC results (dots) are compared with the exact solution (full line). We take ${ϵ}_d=\Gamma$ and consider a flat density of states in the leads with a half bandwidth $10\Gamma$. The increasing error bars for larger times is due to the limited simulation time.

Figure 3

(Color online) Zero-temperature differential conductance $dI/dV$ (in unit of $e^2/h$) for bias values $eV$ around ${\omega }_0=2.0\Gamma$. Electron-phonon coupling is $g=0.5{\omega }_0$. We consider two different values of the fermionic level position ${\epsilon }_d$ in order to reproduce the crossover from reduced (step-down) to enhanced (step-up) conductance.