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

• Published in: arXiv.org 2021-06
• Main Authors: Culver, Adrian B, Natan Andrei
• Format: Article
• Language: English
• Subjects: Evolution; Ferromagnetism; Kondo temperature; Plasma; Steady state; Time dependence; Wave functions
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1912.00281

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