Merging Features from Green’s Functions and Time Dependent Density Functional Theory: A Route to the Description of Correlated Materials out of Equilibrium?

We propose a description of nonequilibrium systems via a simple protocol that combines exchange-correlation potentials from density functional theory with self-energies of many-body perturbation theory. The approach, aimed to avoid double counting of interactions, is tested against exact results in Hubbard-type systems, with respect to interaction strength, perturbation speed and inhomogeneity, and system dimensionality and size. In many regimes, we find significant improvement over adiabatic time dependent density functional theory or second Born nonequilibrium Green’s function approximations. We briefly discuss the reasons for the residual discrepancies, and directions for future work.

Figure 1

XC potentials from the 1D (left) and 3D (right) homogeneous Hubbard model.

Figure 2

Time dependent density at the central site of a $5^3$-site cluster (panel c) for $U=8$ (top row) and $U=24$ (middle row), for slow (left column) and fast regime (right column). The effective cluster is displayed in panel d. The interacting and perturbed site of the cluster is colored in orange. The perturbations $V_{\mathrm{ext}}$ are shown in the bottom row.

Figure 3

Time evolution of the density $n_3$ at site 3 in a $L=8$ Hubbard ring with $U=4$, under the perturbation $V_{\mathrm{ext}}(l,t)$. The parameters for the perturbation profile are $t_0=0$, $\sigma =1$ for the step ($s$), $t_0=5.5$, $\sigma =0.5$ for the ramp ($r$), and $t_0=2.5$, $\sigma =\sqrt{0.4}$ for the Gaussian (g).

Figure 4

Single-impurity, one-orbital Anderson model with $U=2$ (shown in panel e). a): Linear conductance $G$ in the wide-band-limit for ${\mathrm{\Gamma }}_{\mathrm{WBL}}=0.09$ (strong correlations). The exact $G$ is displayed, together with the Hartree-Fock (HF), 2BA, ALDA and hybrid-method results. The density/spin-channel $n/2$ at the impurity is also shown (dashed line). $n/2$ and $G$ share the same vertical scale (in different units). b-e): Time dependent density $n$ (b, c) and average current $=(j_L+j_R)/2$ (d, e) for the Anderson impurity with constant impurity gate voltage $V_{\text{gate}}={\epsilon }_0=0.25$ and bias $b_L(t)=0.5\theta (t)$. The hopping parameter in the leads is $V=1$, the impurity-lead coupling is $V_{\text{link}}=0.5$ (b,d) and $V_{\text{link}}=0.3$ (c,e).