Many-body wavefunctions for quantum impurities out of equilibrium. I. The nonequilibrium Kondo model (original) (raw)
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Many-body wavefunctions for quantum impurities out of equilibrium
Physical review, 2021
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 (F) K = De − 3π 2 8 ρ|J | (J < 0, ρ|J| → ∞). In this regime, the differential conductance dI/dV reaches the unitarity limit 2e 2 /h asymptotically at large voltage or temperature.
Universal aspects of nonequilibrium currents in a quantum dot
Physical Review B, 2006
We study the electric current in the non-equilibrium Kondo model at zero magnetic field, using real-time perturbation theory in the Schwinger-Keldysh formulation. We show that the perturbative coefficients to all orders have a finite limit at large switch-on time (t0 → −∞), and we give a prescription for general operators to give finite coefficients in this limit. We explain how this is related to the fact that the leads play the role of thermal baths and allow relaxation to occur and the steady state to form. This proves perturbatively that a steady state is reached in the Schwinger-Keldysh formulation, and specifies which operators correspond to quantities that have a well-defined value in the steady state. Then, we show that the steady state can be described by a special type of density matrix (related to Hershfield's conjecture for the particular example of the non-equilibrium Kondo model.) In the second part of the paper we perform a renormalization-group analysis of the perturbative series. We give a general argument that strongly suggests that the perturbative series of any average in the steady state satisfies the equilibrium Callan-Symanzik equations, and show in detail how it works to one-loop order for the electric current operator inside any average. We finally compute to two loops order the average of the electric current in the steady state, and perform a renormalization-group improvement. From this, we give a universal prescription, valid in the perturbative regime, for comparing the effect of the electric current to that of the temperature on the "Kondo cloud".
Nonperturbative Approach to the Nonequilibrium Kondo Model
arXiv: Strongly Correlated Electrons, 2019
We present a nonperturbative method for calculating the time-dependent many body wavefunction that follows a local quench, and we use it to find the exact time evolution of the nonequilibrium Kondo model driven by a bias voltage. 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. We find a series expression for the steady state current; it agrees with standard leading order results in the usual weak antiferromagnetic regime and exhibits a new universal regime of strong ferromagnetic coupling, with Kondo temperature TK=Defrac3pi28rhoJT_K= D e^{\frac{3\pi^2}{8 } \rho J}TK=Defrac3pi28rhoJ. In this regime, the differential conductance dI/dVdI/dVdI/dV reaches the unitarity limit 2e2/h2e^2/h2e2/h asymptotically at large voltage or temperature.
Oscillatory nonlinear conductance of an interacting quantum wire with an impurity
2003
The nonlinear conductance of a one-dimensional quantum wire adiabatically coupled to Fermi liquid electron reservoirs is determined in presence of an impurity. We show that electron-electron interaction in connection with the finite length of the wire leads to characteristic oscillations in the current as a function of the applied voltage.
Nonequilibrium dynamics of the Anderson impurity model
Physical Review B, 1998
The M-channel Anderson impurity model (M = 1, 2) is studied in the Kondo limit with a finite voltage bias applied to the conduction electron reservoirs. Using the Non-Crossing Approximation (NCA), we calculate the local spectral functions, the differential conductance, and susceptibility at non-zero bias for symmetric as well as asymmetric coupling of the impurity to the leads. We describe an effective procedure to solve the NCA integral equations which enables us to reach temperatures far below the Kondo scale. This allows us to study the scaling regime where the conductance depends on the bias only via a scaling function. Our results are applicable to both tunnel junctions and to point contacts. We present a general formula which allows one to go between the two cases of tunnel junctions and point contacts. Comparison is also made between the conformal field theory and the NCA conduction electron self-energies in the two channel case.
Physical Review B
Nonlinear tunneling current through a quantum dot (an Anderson impurity system) subject to both constant and alternating electric fields is studied in the Kondo regime. A systematic diagram technique is developed for perturbation study of the current in physical systems out of equilibrium governed by time-dependent Hamiltonians of the Anderson and the Kondo models. The ensuing calculations prove to be too complicated for the Anderson model, and hence, a mapping on an effective Kondo problem is called for. This is achieved by constructing a time-dependent version of the Schrieffer-Wolff transformation. Perturbation expansion of the current is then carried out up to third order in the Kondo coupling J yielding a set of remarkably simple analytical expressions for the current. The zero-bias anomaly of the direct current (dc) differential conductance is shown to be suppressed by the alternating field while side peaks develop at finite source-drain voltage. Both the direct component and ...
Conductance quantization and dissipation
2003
We have calculated the conductance in the low-temperature linear-response regime for a quantum point contact (QPC) in the WKB approximation. Our calculation shows that the inclusion of dissipation in a consistent manner is equally able to produce the Landauer-Büttiker results. Furthermore our result shows that there is no need for the assumption of ballistic transport or assigning different chemical potentials to left-and right-reservoirs.
Low-temperature transport through a quantum dot: Finite-U results and scaling behavior
Physical Review B, 2002
The infinite-U Anderson model is applied to non-equilibrium transport through a quantum dot containing two spin levels weakly coupled to two leads. At low temperatures, the Kondo peak in the equilibrium density of states is split upon the application of a voltage bias. The split peaks, one at the chemical potential of each lead, are suppressed by non-equilibrium dissipation. In a magnetic field, the Kondo peaks shift away from the chemical potentials by the Zeeman energy, leading to an observable peak in the differential conductance when the non-equilibrium bias equals the Zeeman energy. PACS numbers: 72.15.Qm 73.40.Gk 73.20.Dx 73.50.Fq 1