Nonequilibrium electron transport using the density matrix renormalization group method

We extended the density matrix renormalization group method to study the real time dynamics of interacting one-dimensional spinless Fermi systems by applying the full time evolution operator to an initial state. As an example we describe the propagation of a density excitation in an interacting clean system and the transport through an interacting nano structure.

Figure 1

(Color online) Time evolution of a wave packet for a system of $M=30$ sites, periodic boundary conditions, and $V=0.0$ (plus), $V=1.0$ (crosses) and $V=2.0$ (stars). The snapshots are taken at $t_j=0$, 2, 5, and 8. $n_{\text{Cut}}=300$ states per block were kept within the DMRG procedure.

Figure 2

(Color online) (a) Initial wave packet for a 50 site system with periodic boundary conditions and $V=1$, for different numbers of states kept per block: $n_{\text{Cut}}=100$ (plus), 200 (crosses), 500 (stars) and 750 (open squares), extracted from a simulation with $T=20$ and time steps $t_j-t_{j-1}=1$. (b) Same system at time step $t_j=8$.

Figure 3

(Color online) Nano structure attached to leads.

Figure 4

(Color online) Transport through an interacting region of $M_S=7$ sites and $M_L=43$ lead sites, hard wall boundary conditions and $n_{\text{Cut}}=1000$. The snapshots are taken at $T=0$,3,7,12. The density is averaged over two neighboring sites to smoothen $2k_F$ oscillations and is plotted vs the site location $x$ for $V=0$ (plus), $V=1$ (crosses), $V=2$ stars, and $V=5$ (squares). For $V=0$ the line is calculated by an exact diagonalization.