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

TL;DR

This paper introduces a numerical method to analyze steady-state transport in one-dimensional correlated quantum systems, combining classical finite-size analysis with quantum dynamics simulations to accurately determine current-voltage characteristics.

Contribution

The authors develop a novel approach that links transient finite-system currents to steady-state transport, validated through the spinless fermion model and comparison with theoretical predictions.

Findings

Numerical results match exact solutions for non-interacting fermions.

In the linear regime, current is independent of setup and agrees with Luttinger liquid theory.

At higher voltages, current depends on the setup, showing negative differential conductance and saturation effects.

Abstract

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 non-equilibrium 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-neighbour 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 non-interacting 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.