Numerical method for nonlinear steady-state transport in one-dimensional correlated conductors

We present a method for investigating the steady-state transport properties of one-dimensional correlated quantum systems. Using a procedure based on our analysis of finite-size effects in a related classical model (LC line) we show that stationary currents can be obtained from transient currents in finite systems driven out of equilibrium. The nonequilibrium dynamics of correlated quantum systems is calculated using the time-evolving block decimation method. To demonstrate our method we determine the full I-V characteristic of the spinless fermion model with nearest-neighbor hopping t(H) and interaction V-H using two different setups to generate currents (turning on/off a potential bias). Our numerical results agree with exact results for noninteracting fermions (V-H = 0). For interacting fermions we find that in the linear regime eV << 4t(H) the current I is independent from the setup and our numerical data agree with the predictions of the Luttinger liquid theory combined with the Bethe Ansatz solution. For larger potentials V the steady-state current depends on the current-generating setup and as V increases we find a negative differential conductance with one setup while the currents saturate at finite values in the other one. Both effects are due to finite renormalized bandwidths.