Many-body wavefunctions for quantum impurities out of equilibrium

TL;DR

This paper introduces a new method for calculating the time-dependent wavefunction of quantum impurity systems out of equilibrium, applied to the Kondo model, revealing universal regimes and steady-state properties without using Bethe ansatz.

Contribution

The authors develop a Bethe ansatz-free approach to compute the exact time-evolving wavefunction for quantum impurity models, applicable to various models including the Kondo and Anderson impurities.

Findings

Exact wavefunction for the nonequilibrium Kondo model after a quench.

Universal strong ferromagnetic coupling regime with conductance reaching unitarity.

Series expansion for current converging to steady state results.

Abstract

We present a method for calculating the time-dependent many-body wavefunction that follows a local quench. We apply the method to the voltage-driven nonequilibrium Kondo model to find the exact time-evolving wavefunction following a quench where the dot is suddenly attached to the leads at $t=0$. The method, which does not use Bethe ansatz, also works in other quantum impurity models (we include results for the interacting resonant level and the Anderson impurity model) and may be of wider applicability. In the particular case of the Kondo model, we show that the long-time limit (with the system size taken to infinity first) of the time-evolving wavefunction is a current-carrying nonequilibrium steady state that satisfies the Lippmann-Schwinger equation. We show that the electric current in the time-evolving wavefunction is given by a series expression that can be expanded either in weak coupling or in strong coupling, converging to all orders in the steady-state limit in either case. The series agrees to leading order with known results in the well-studied regime of weak antiferromagnetic coupling and also reveals another universal regime of strong ferromagnetic coupling, with Kondo temperature $T_K^{(F)} = D e^{-\frac{3\pi^2}{8} \rho |J|}$ ($J<0$, $\rho|J|\to\infty$). In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$ asymptotically at large voltage or temperature.