TY - JOUR

T1 - Many-body wavefunctions for quantum impurities out of equilibrium. I. The nonequilibrium Kondo model

AU - Culver, Adrian B.

AU - Andrei, Natan

N1 - Funding Information:
We are grateful to Chung-Hou Chung, Piers Coleman, Garry Goldstein, Yashar Komijani, Yigal Meir, Andrew Mitchell, Achim Rosch, and Hubert Saleur for helpful discussions. We have benefited from working on related problems with Huijie Guan, Paata Kakashvili, Christopher Munson, and Roshan Tourani. A.B.C. acknowledges support from the Samuel Marateck Fellowship in Quantum Field Theory Physics and the Excellence Fellowship (both from Rutgers University). This material is based upon work supported by the National Science Foundation under Grant No. 1410583.
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/5/4

Y1 - 2021/5/4

N2 - We present here the details of a method [A. B. Culver and N. Andrei, Many-body wavefunctions for quantum impurities out of equilibrium, Phys. Rev. B 103, L201103 (2021)10.1103/PhysRevB.103.L201103] 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 TK(F)=De-3π28ρ|J| (J<0, ρ|J|→ ∞). In this regime, the differential conductance dI/dV reaches the unitarity limit 2e2/h asymptotically at large voltage or temperature.

AB - We present here the details of a method [A. B. Culver and N. Andrei, Many-body wavefunctions for quantum impurities out of equilibrium, Phys. Rev. B 103, L201103 (2021)10.1103/PhysRevB.103.L201103] 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 TK(F)=De-3π28ρ|J| (J<0, ρ|J|→ ∞). In this regime, the differential conductance dI/dV reaches the unitarity limit 2e2/h asymptotically at large voltage or temperature.

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U2 - 10.1103/PhysRevB.103.195106

DO - 10.1103/PhysRevB.103.195106

M3 - Article

AN - SCOPUS:85106029236

SN - 0163-1829

VL - 103

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

IS - 19

M1 - 195106

ER -