Auxiliary Master Equation for Nonequilibrium Dual-Fermion Approach

We introduce an auxiliary quantum master equation dual fermion method and argue that it presents a convenient way to describe steady states of correlated impurity models. The scheme yields an expansion around a reference that is much closer to the true nonequilibrium state than that in the original dual fermion formulation. In steady-state situations, the scheme is numerically inexpensive and avoids time propagation. The Anderson impurity model is used to test the approach against numerically exact benchmarks.

Figure 1

Nonequilibrium junction model. Shown are (a) Anderson impurity model, (b) reference system within original DF approach [41], and (c) reference system within auxiliary QME-DF approach.

Figure 2

Steady-state transport characteristics vs gate voltage at fixed bias. Shown are (a) population and (b) current vs level position, as calculated from auxiliary QME (dotted line), and zero- (dashed line) and first- (solid line) order QME-DF approaches. Circles (red) represent results of numerically exact TDDMRG simulations. The inset in panel (a) shows the results of the original nonequilibrium DF simulation, where, at $t=0$, coupling between system and contacts is switched on for several level positions.

Figure 3

Current voltage characteristics. We show the auxiliary QME (dotted line), zero (dashed line), and first (solid line) order QME-DF approaches. For comparison, circles and squares represent, respectively, TDDMRG and CT-QMC results.

Figure 4

Spectral function of Anderson impurity model. Shown are results of QME-DF simulations for (a) the spectral function of the unbiased ($V_{sd}=0$, solid line) and biased junction ($V_d/V_0=2.5$, dotted line), and (b) The spectral function vs energy and applied bias.