Many-body wavefunctions for quantum impurities out of equilibrium. I. The nonequilibrium Kondo model

TL;DR

This paper introduces a method for calculating the exact time-dependent wavefunction of quantum impurity models out of equilibrium, applied specifically to the Kondo model, revealing universal conductance behavior at strong ferromagnetic coupling.

Contribution

It presents a new method for computing the nonequilibrium wavefunction of quantum impurity systems without Bethe ansatz, applicable to various models and regimes.

Findings

Long-time wavefunction approaches a nonequilibrium steady state.

Series expansion of current converges to known results in weak coupling.

Universal conductance limit reached at high voltage or temperature.

Abstract

We present here the details of a method [A. B. Culver and N. Andrei, Phys. Rev. B 103, L201103 (2021)] 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 and may be of wider applicability. We show that the long-time limit (with the system size taken to infinity first) of the time-evolving wavefunction of the Kondo model 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 a 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.