Twofold Advance in the Theoretical Understanding of Far-From-Equilibrium Properties of Interacting Nanostructures

We calculate the full $I\mathrm{\text{−}}V$ characteristics at vanishing temperature in the self-dual interacting resonant level model in two ways. The first uses careful time dependent density matrix renormalization group with a large number of states per block and a representation of the reservoirs as leads subjected to a chemical potential. The other is based on integrability in the continuum limit, and generalizes early work by Fendley, Ludwig, and Saleur on the boundary sine-Gordon model. The two approaches are in excellent agreement, and uncover among other things a power law decay of the current at large voltages when $U>0$.

Figure 1

Current versus source drain voltage $V_{\mathrm{SD}}$ for a hybridization of $t^{\prime }=0.5$, and interaction values of $U=-1.0$, 0.0, 0.3, 1.0, 5.0, and 10.0. The subscript “1” (“2”) of $I$ refers to data extrapolated from link to the left (right) lead. The lines are guides to the eye, except for $U=0.0$ where we plotted the exact result for infinite leads. Calculations have been performed with 96 sites, 48 fermions keeping at least 2000 states per DMRG block. In addition, data for $U=1.0$, $M=120$ sites and $N_{\mathrm{cut}}=3000$ states per block are shown.

Figure 2

Comparison between analytical and DMRG results at the self-dual point. The numerical data have been fitted using a single parameter $T_B=c(t^{\prime }{)}^{4/3}$, $c\approx 2.7$.

Figure 3

Exponents in the negative differential conductance regime for $t^{\prime }=0.2$, 0.3, 0.4, and 0.5.