Nonequilibrium Transport in Quantum Impurity Models: The Bethe Ansatz for Open Systems

We develop an exact nonperturbative framework to compute steady-state properties of quantum impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates which satisfy an appropriate Lippman-Schwinger equation. Introducing a generalization of the equilibrium Bethe ansatz—the nonequilibrium Bethe ansatz—we explicitly construct the scattering eigenstates for the interacting resonance level model and derive exact, nonperturbative results for the steady-state properties of the system.

Figure 1

There are two types of single-particle scattering states. In a type 1 scattering state, an incoming electron in lead 1 is scattered by the impurity and can hop onto either lead 1 or lead 2.

Figure 2

Here we show the current as a function of voltage for various $U$ with ${\mu }_{1/2}={ϵ}_d\pm V/2$ for fixed bandwidth $D$ and $\Delta$. Note that the current is not monotonic in $U$. We also show the distribution in lead 1 as a function of momentum for various voltages, where, without loss of generality, we take $k_o^1=0$.